MIME-Version: 1.0 Content-Type: multipart/related; boundary="----=_NextPart_01C82DF7.23E03F50" This document is a Single File Web Page, also known as a Web Archive file. If you are seeing this message, your browser or editor doesn't support Web Archive files. Please download a browser that supports Web Archive, such as Microsoft Internet Explorer. ------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Notation and Algebra of Functions

This presentation contains content that your browser may not be able to = show properly. This presentation was optimized for more recent versions of Micro= soft Internet Explorer.

If you would like to proceed anyway, click here.

 ------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/master06.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii"
Click to edit Master title style
Clic= k to edit Master text styles
Sec= ond level
Thi= rd level
Fou= rth level
Fif= th level
‹date/time›&= #13;
‹footer›
‹#›
------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/master06.xml Content-Transfer-Encoding: quoted-printable Content-Type: text/xml; charset="utf-8" ------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/preview.wmf Content-Transfer-Encoding: base64 Content-Type: image/x-wmf AQAJAAAD6wAAAAYAOQAAAAAABAAAAAMBCAAFAAAACwIAAAAABQAAAAwCeQChAAMAAAAeAAcAAAD8 AgAA////AAAABAAAAC0BAAAIAAAA+gIFAAAAAAD///8ABAAAAC0BAQAOAAAAJAMFAP///////3gA oAB4AKAA////////CAAAAPoCAAAAAAAAAAAAAAQAAAAtAQIABwAAAPwCAAD///8AAAAEAAAALQED AAQAAAAnAf//HAAAAPsC9/8AAAAAAACQAQAAAAAAQAAAQXJpYWwAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAEAAAALQEEAAQAAAAuARgABAAAAAIBAQAFAAAACQIAAAACOQAAADIKEQALACEAAABO b3RhdGlvbiBhbmQgQWxnZWJyYSBvZiBGdW5jdGlvbnP/BwAFAAMABAADAAIABQAFAAMABAAFAAUA AwAGAAIABQAFAAUAAwAEAAMABAADAAIABgAFAAUABAADAAIABQAEAAUABAAAAC4BAAAcAAAA+wIQ AAcAAAAAALwCAAAAAAECAiJTeXN0ZW0AAAAAAAAAAAAAGAAAAAIAAACYOhUA5AQAAAQAAAAtAQUA BAAAAPABBAADAAAAAAA= ------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/pres.xml Content-Transfer-Encoding: quoted-printable Content-Type: text/xml; charset="utf-8" ------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0077.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Notation and Algebra of Functions
Notation and Algebra of Functions
------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0078.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Notation and Algebra of Functions
Notation and Algebra of Functions
A function= is a procedure that prod= uces
exactly one output for each (legitim= ate)
input.
------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0079.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Notation and Algebra of Functions
Notation and Algebra of Functions
A function is a procedure that produces
exactly one output for ea= ch (legitimate)
input.
Example:  Are the following functions? =
a.  Input a number x, the output is (are)
whole number(s) within ¾ of x.
  
 
------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0080.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Notation and Algebra of Functions
Notation and Algebra of Functions
A function is a procedure that produces
exactly one output for each (legitim= ate)
input.
Example:  Are the following functions? =
a.  Input a number x, the output is (are)
whole numbe= r(s) within ¾ of x.    No.
------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0081.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Notation and Algebra of Functions
Notation and Algebra of Functions
A function is a procedure that produces
exactly one output for ea= ch (legitimate)
input.
Example:  Are the following functions? =
a.  Input a number x, the output is (are)
whole number(s) within ¾ of x.    No.
b.  Input a number x, the output is (= are)
the smallest whole number= (s) that’s more
than x.
  
 
------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0082.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Notation and Algebra of Functions
Notation and Algebra of Functions
A function is a procedure that produces
exactly one output for each (legitim= ate)
input.
Example:  Are the foll= owing functions?
a.  Input a number x, = the output is (are)
whole number(s) within ¾ of x.    No.
b.  Input a number x, = the output is (are)
the smallest whole number(s) that’s more
than x.  Yes.
  
 
------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0083.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Notation and Algebra of Functions
Notation and Algebra of Functions
A <= /span>function= is a procedure that produces
exactly one output for each (legitimate) input. 
Often functions are given as mathematics formulas.
------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0084.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Notation and Algebra of Functions
Notation and Algebra of Functions
A function is a procedure that produces
exactly one output for each (legitimate) input. 
Often functions are given as mathematics formulas.
Domain: The set of all the legitimate inputs is called the <= /i>domain of the function.<= /span>
------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0085.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Notation and Algebra of Functions
Notation and Algebra of Functions
Mathema= tics functions are often named as f, g, h.., the input is represented by x and the = output as y. <= /span>
=
------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0086.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Notation and Algebra of Functions
Notation and Algebra of Functions
Mathematics functions are often named as= f, g, h.., the input is represented by x and the output = as y.
Example:   
        = ;  f (X) =3D X2 – 2X + 3 =3D y
        = ;       
------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0087.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Notation and Algebra of Functions
Notation and Algebra of Functions
Mathematics functions are often named as f, g, h.., = the input is represented by x and the output as y. &= #13;
Example:    <= /span>  
        = ;  f (X) =3D X2 – 2X + 3 =3D y
name of        = ;       
the function
------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0087_image001.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhFQApAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEABAAP ACMAgAAAAACZmQI7hI8YyRbbznvRTdgureDyvmDZxpGlGE0fuKqfWcEjOq7sKzN54p72rgBKaDUc kXcMJoe/pcV5w7WEhgIAOw== ------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0088.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Notation and Algebra of Functions
Notation and Algebra of Functions
Mathema= tics functions are often named as f, g, h.., the input is represented by x and the = output as y. <= /span>
Example:    <= /span>input box 
        = ;  f (X) =3D X2 – 2X + 3 =3D y
name of        = ;      
the function
------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0088_image002.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhFQApAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEABAAP ACMAgAAAAACZmQI7hI8YyRbbznvRTdgureDyvmDZxpGlGE0fuKqfWcEjOq7sKzN54p72rgBKaDUc kXcMJoe/pcV5w7WEhgIAOw== ------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0088_image003.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQAdAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAYAAgAS ABYAgAAAAAAAAAIshI8JEerG2ktxUmavzAvzvmXVN5IeV4qnGlopK0LrE830O9Wto+9K/VkEDwUA Ow== ------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0089.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Notation and Algebra of Functions
Notation and Algebra of Functions
Mathema= tics functions are often named as f, g, h.., the input is represented by x and the = output as y. <= /span>
Example:    <= /span>input box 
        = ;  f (X) =3D X2 – 2X + 3 =3D y
name of        = ;        actual formula
the function
------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0089_image004.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhFQApAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEABAAP ACMAgAAAAACZmQI7hI8YyRbbznvRTdgureDyvmDZxpGlGE0fuKqfWcEjOq7sKzN54p72rgBKaDUc kXcMJoe/pcV5w7WEhgIAOw== ------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0089_image005.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQAdAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAYAAgAS ABYAgAAAAAAAAAIshI8JEerG2ktxUmavzAvzvmXVN5IeV4qnGlopK0LrE830O9Wto+9K/VkEDwUA Ow== ------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0089_image006.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwAfAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMAAwAF ABoAgAAAAP8AAAIXBGKGGtv44juNuUqvtjz36YXgiJGbVwAAOw== ------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0090.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Notation and Algebra of Functions
Notation and Algebra of Functions
Mathema= tics functions are often named as f, g, h.., the input is represented by x and the = output as y. <= /span>
Example:    <= /span>input box 
        = ;  f (X) =3D X2 – 2X + 3 =3D y
name of        = ;        actual formula
the function
The output
------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0090_image007.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhFQApAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEABAAP ACMAgAAAAACZmQI7hI8YyRbbznvRTdgureDyvmDZxpGlGE0fuKqfWcEjOq7sKzN54p72rgBKaDUc kXcMJoe/pcV5w7WEhgIAOw== ------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0090_image008.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQAdAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAYAAgAS ABYAgAAAAAAAAAIshI8JEerG2ktxUmavzAvzvmXVN5IeV4qnGlopK0LrE830O9Wto+9K/VkEDwUA Ow== ------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0090_image009.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwAfAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMAAwAF ABoAgAAAAP8AAAIXBGKGGtv44juNuUqvtjz36YXgiJGbVwAAOw== ------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0090_image010.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhHQAiAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAUABQAX ABsAgAAAAAAAAAI2DI6pe2EMlXOxzlnZfXndrgEYqFGkZ57JqDZpK74tC9OzrNqnvuM9V/OReENh hwhCHo1L4K0AADs= ------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0091.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Notation and Algebra of Functions
Notation and Algebra of Functions
f (X) =3D X2 – 2X + 3=
The = input box holds the input for the formula.
------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0091_image011.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhFAAjAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAUABAAO AB4AgAAAAAAAAAIqTICpaLfbzEtRzjaVc5l2+HkhMwLcd6Jl2rFXaa7yHLrvaD+5Rte9iisAADs= ------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0092.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Notation and Algebra of Functions
Notation and Algebra of Functions
f (X) =3D X2 – 2X + 3=
The = input box holds the input for the formula.
Hence f (2) means to set x to be (2) in the formula, that is
        = ;   
=
------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0092_image012.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhFAAjAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAUABAAO AB4AgAAAAAAAAAIqTICpaLfbzEtRzjaVc5l2+HkhMwLcd6Jl2rFXaa7yHLrvaD+5Rte9iisAADs= ------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0093.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Notation and Algebra of Functions
Notation and Algebra of Functions
f (X) =3D X2 – 2X + 3=
The = input box holds the input for the formula.
Hence f (2) means to set x to be (2) in the formula, that is, <= /div>
        = ;    f (2= ) =3D
 
=
------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0093_image013.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhFAAjAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAUABAAO AB4AgAAAAAAAAAIqTICpaLfbzEtRzjaVc5l2+HkhMwLcd6Jl2rFXaa7yHLrvaD+5Rte9iisAADs= ------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0094.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Notation and Algebra of Functions
Notation and Algebra of Functions
f (X) =3D X2 – 2X + 3=
The = input box holds the input for the formula.
Hence f (2) means to set x to be (2) in the formula, that is, <= /div>
        = ;    f (2= ) =3D (2)2 – 2(2) + 3
 
=
------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0094_image014.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhFAAjAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAUABAAO AB4AgAAAAAAAAAIqTICpaLfbzEtRzjaVc5l2+HkhMwLcd6Jl2rFXaa7yHLrvaD+5Rte9iisAADs= ------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0095.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Notation and Algebra of Functions
Notation and Algebra of Functions
f (X)= =3D X2 – 2X + 3=
The input box holds the input for the formula.
= Hence f (2) means to set= x to be (2) in the formula, that is,
        = ;    f (2= ) =3D (2)2 – 2(2) + 3
        = ;     f (2) =3D 3 =3D y=
 
        = ;          the output  
------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0095_image015.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhFAAjAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAUABAAO AB4AgAAAAAAAAAIqTICpaLfbzEtRzjaVc5l2+HkhMwLcd6Jl2rFXaa7yHLrvaD+5Rte9iisAADs= ------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0095_image016.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwAjAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMAAwAH AB8AgAAAAAAAAAIgBGJ5mOHqnomPqnlPZnBnfXGNF5KdOZbqyaarC2PvVAAAOw== ------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0109.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Notation and Algebra of Functions
Notation and Algebra of Functions
We = may input expressions.
 
------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0110.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Notation and Algebra of Functions
Notation and Algebra of Functions
We = may input expressions.
Example:
Give= n f(X) =3D X2 – 2X + 3, simplify f = (2a) and
f (a+b).
------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0111.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Notation and Algebra of Functions
Notation and Algebra of Functions
We may input expressions.
Example:
Give= n f(X) =3D X2 – 2X + 3, simplify f = (2a) and
f (a+b).
f (2a) =3D
=
------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0112.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Notation and Algebra of Functions
Notation and Algebra of Functions
We may input expression.
Example:
Give= n f(X) =3D X2 – 2X + 3, simpl= ify f = (2a) and
f (a+b).
f (2a) = =3D= (2a)2 – 2(2a) + 3
------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0113.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Notation and Algebra of Functions
Notation and Algebra of Functions
We may input expressions.
Example:
Give= n f(X) =3D X2 – 2X + 3, simpl= ify f = (2a) and
f (a+b).
f (2a) =3D = (2a)2 – 2(2a) + 3
         =3D 4a– 4a= + 3
------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0114.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Notation and Algebra of Functions
Notation and Algebra of Functions
We may input expressions.
Example:
Give= n f(X) =3D X2 – 2X + 3, simplify f (2a) and
f (a+b).
f (2a) =3D = (2a)2 – 2(2a) + 3
         =3D 4a– 4a= + 3
f (a+b= ) =3D
------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0115.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Notation and Algebra of Functions
Notation and Algebra of Functions
We may input expressions.
Example:
Give= n f(X) =3D X2 – 2X + 3, simpl= ify f (2a) and
f (a+b).
f (2a) =3D = (2a)2 – 2(2a) + 3
         =3D 4a– 4a= + 3
f (a+b) =3D (a+b= )2 – 2(a+b) + 3
------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0117.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Notation and Algebra of Functions
Notation and Algebra of Functions
We may input expressions.
Example:
Give= n f(X) =3D X2 – 2X + 3, simpl= ify f = (2a) and
f (a+b).
f (2= a) =3D= (2a)2 – 2(2a) + 3
         =3D 4a2 – 4a + 3 <= /div>
f (a+b) =3D (a+b)2 – 2(a+b) + 3
        = ;   =3D a2 + 2ab + b2 – 2a – 2b= + 3
------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0117_image017.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhiAAcAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAACG ABwAgAAAAAAAAAJ1jI+py+0Po5wT2Iuz3rz7D4biCBrkiabquprsC8fy5872jZN1zvf97gsKX8Ch 8RgqIpfMi7IJNT6j1F+gih1Os1zYtgtOfcNk0biM7pzTbMy63X7D0/J5uW4P4/PdPT/r91cVKBhF WNh0iLhE0ej4CBkpaVAAADs= ------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0117_image018.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhIwEhAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAAAi ASEAgAAAAAAAAALBRI6py+0Po5y02ouz3nyCD4biSJbmiabqyrbuC8fyTKdHjef6zvf+DwTdgsSi 8YhM7obKpvMJjeKY0qr1ik1Ss9yu97vagsfkslVsTqvXPzT7DY+z3PK6vU6/6/flPP8PeOUXSFio FWCYqNg0uOj4KNMIOUmJIlmJmWmAqNnpKXL5KVoYOmrKV3qqise56mqY+iprFjtr+1V7q4uVu+sb 1fsrrBQ8bFxUfKzsk7zsnNP8LB252WF9jZ2tvc3d7X1QAAA7 ------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0118.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Notation and Algebra of Functions
Notation and Algebra of Functions
We may +, – , * , and / functions.
=
------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0119.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Notation and Algebra of Functions
Notation and Algebra of Functions
We may +, – , * , and / functions.
Example: Let f(x) =3D 3x – 4, g(x) =3D= x2 – 2x – 3, find:
f+g, f – g, f*g, and f/g. <= /div>
 
=
------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0120.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Notation and Algebra of Functions
Notation and Algebra of Functions
We may +, – , * , and / functions.
Example: Let f(x) =3D 3x – 4, g(x) =3D= x2 – 2x – 3, find:
f+g, f – g, f*g, and f/g. <= /div>
 
f+g =3D 3x – 4 + x<= /span>2 – 2x – 3 =3D x2 + x – 7
 
------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0121.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Notation and Algebra of Functions
Notation and Algebra of Functions
We may +, – , * , and / functions.
Example: Let f(x) =3D 3x – 4, g(x) =3D= x2 – 2x – 3, find:
f+g, f – g, f*g, and f/g. <= /div>
 
f+g =3D 3x – 4 + x2 – 2x – 3 =3D x2 + x – 7
f – g =3D 3x – 4 – (x2 – 2x – 3)
       
------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0122.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Notation and Algebra of Functions
Notation and Algebra of Functions
We may +, – , * , and / functions.
Example: Let f(x) =3D 3x – 4, g(x) =3D= x2 – 2x – 3, find:
f+g, f – g, f*g, and f/g. <= /div>
 
f+g =3D 3x – 4 + x2 – 2x – 3 =3D x2 + x – 7
f – g =3D 3x – 4 – (x2 – 2x – 3)
        =3D 3x – 4 – x2 + 2x + 3
------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0123.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Notation and Algebra of Functions
Notation and Algebra of Functions
We may +, – , * , and / functions.
Example: Let f(x) =3D 3x – 4, g(x) =3D= x2 – 2x – 3, find:
f+g, f – g, f*g, and f/g. <= /div>
 
f+g =3D 3x – 4 + x2 – 2x – 3 =3D x2 + x – 7
f – g =3D 3x – 4 – (x2 – 2x – 3)
        =3D 3x – 4 – x2 + 2x + 3 =3D -x2 + 5x – 1
=
------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0124.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Notation and Algebra of Functions
Notation and Algebra of Functions
We may +, – , * , and / functions.
Example: Let f(x) =3D 3x – 4, g(x) =3D= x2 – 2x – 3, find:
f+g, f – g, f*g, and f/g. <= /div>
 
f+g =3D 3x – 4 + x2 – 2x – 3 =3D x2 + x – 7
f – g =3D 3x – 4 – (x2 – 2x – 3)
        =3D 3x – 4 – x2 + 2x + 3 =3D -x2 + 5x – 1
f*g =3D (3x – 4)*(x2 – 2x – 3)
------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0125.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Notation and Algebra of Functions
Notation and Algebra of Functions
We may +, – , * , and / functions.
Example: Let f(x) =3D 3x – 4, g(x) =3D= x2 – 2x – 3, find:
f+g, f – g, f*g, and f/g. <= /div>
 
f+g =3D 3x – 4 + x2 – 2x – 3 =3D x2 + x – 7
f – g =3D 3x – 4 – (x2 – 2x – 3)
        =3D 3x – 4 – x2 + 2x + 3 =3D -x2 + 5x – 1
f*g =3D (3x – 4)*(x2 – 2x – 3) =3D 3x3 ̵= 1; 10x2 – x + 12
=
------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0126.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Notation and Algebra of Functions
Notation and Algebra of Functions
We may +, – , * , and / functions.
Example: Let f(x) =3D 3x – 4, g(x) =3D x2 – 2x – 3, find:
f+g, f – g, f*g, and f/g.
 
f+g = =3D 3x – 4 + x2 – 2x – 3 =3D x2 + x – 7
f = 211; g =3D 3x – 4 – (x2 – 2x – 3) <= /span>
        =3D 3x – 4 – x2 + 2x + 3 =3D -x2 + 5x – 1
f*g = =3D (3x – 4)*(x2 – 2x – 3) =3D 3x3 ̵= 1; 10x2 – x + 12
f/g = =3D (3x – 4)/ (x2 – 2x – 3)
------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0126_image019.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlh5QAmAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQDk ACQAgAAAAAAAAAKzjI+py+0Po5y02osv2Lz7D4biSJbmiabqyrap4cbyTNf2jQNwzvf+D8ztgsSi 8fgbIpfMpjOkfEqn1F60is1qUdet9+vtgsdkp7iMTgPP6rabxn7L59wA/Y5/2fP8/ifuF9gGKFhI RmiYuIWo2EjF6BjZBClZaURpmZm0p9lpxukZeoQpWupCapqqp8rKg9oKC/IaS7sxWxt7i9uqu6va 62sKHCw6TOyZkay8zNzs/AyNUAAAOw== ------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0126_image020.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlh0wCDAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAADS AIIAgAAAAAAAAAL/jI+py+0PIwS02ouz3rz7D1JBSJbmSY7oyrao6sayC8/2/eL6rtX8DwT4gsTW sIikJZc5pnN1fEov0akVU70+s9ort5v8grdjrbi8PKN56jWx7b7B42y6c27H4fOsPV/m92cSKNhX +HbIRJjosciY8lgXiTipVxnkeGmRqdnTOcP5SSUaE0oqcmqUamN62Ur6Ohn7OftYq3mbmFu5W9gb +fsXzDicV3x4TJcsuOzWzPeMFm03PVYdd92VvbbttQoqES4+Tl5+8I2err7O3u7+Dh8vP09fb3+P n6+/z9/v/w8woMCBBAsaPIgwocKFDBs6fAgxosSJFCtavIgxnrmN5xw7eiy3qlsnkaUsklRS8aSq lCFNtmSZSqWslxRlQnEZE+cpm7ZoTuR5AqgunxKFljDqi2hEpCGYClMK0ekHqcagPqTaAasyqw61 bvDqjGtDsBnIShPL0OwomDt1wnIrSq21kB/r2r3bMaPevXz7+h2LN7DgwYQLTyj7l5mnxNAWM6bm +DG2yJK5Ua5cJorcpZcxg9HsOSzi0GdHk55r+rS2zqqlgG69OjXsKa9nW6lt2zXr3Ehw81a0+zem 4MJ/+C5e5Djy4bKXM8fiPAzx6KymUwdk/TpK6NqBKO9evazh8eTLmxdXAAA7 ------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0059.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Notation and Algebra of Functions
Notation and Algebra of Functions
Expression can be made = using functions notations.        = ;   
------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0060.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Notation and Algebra of Functions
Notation and Algebra of Functions
Expression can be made = using functions notations.        = ;   
Examp= le:  Let f(x) =3D x2 – 2x – 3, g(x) =3D 2x + 1.
a.Simplify f(2) – g(-3)&= #13;
------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0061.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Notation and Algebra of Functions
Notation and Algebra of Functions
Expression can be made = using functions notations.        = ;   
Examp= le:  Let f(x) =3D x2 – 2x – 3, g(x) =3D 2x + 1.
a.Simplify f(2) – g(-3)&= #13;
      f<= span lang=3DEN-US style=3D'color:red;mso-fareast-language:ZH-CN'>(2) =3D (2)2 – 2*(2) R= 11; 3
        = ;    
    
------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0062.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Notation and Algebra of Functions
Notation and Algebra of Functions
Expression can be made = using functions notations.        = ;   
Examp= le:  Let f(x) =3D x2 – 2x – 3, g(x) =3D 2x + 1.
a.Simplify f(2) – g(-3)&= #13;
      f<= span lang=3DEN-US style=3D'color:red;mso-fareast-language:ZH-CN'>(2) =3D (2)2 – 2*(2) R= 11; 3
        = ;     =3D 4 – 4 – 3
------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0063.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Notation and Algebra of Functions
Notation and Algebra of Functions
Expression can be made = using functions notations.        = ;   
Examp= le:  Let f(x) =3D x2 – 2x – 3, g(x) =3D 2x + 1.
a.Simplify f(2) – g(-3)&= #13;
      f<= span lang=3DEN-US style=3D'color:red;mso-fareast-language:ZH-CN'>(2) =3D (2)2 – 2*(2) R= 11; 3
        = ;     =3D 4 – 4 – 3
        = ;     =3D -3
------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0064.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Notation and Algebra of Functions
Notation and Algebra of Functions
Expression can be made = using functions notations.        = ;   
Examp= le:  Let f(x) =3D x2 – 2x – 3, g(x) =3D 2x + 1.
a.Simplify f(2) – g(-3)&= #13;
      f<= span lang=3DEN-US style=3D'color:red;mso-fareast-language:ZH-CN'>(2) =3D (2)2 – 2*(2) R= 11; 3     g= (-3) =3D 2(-3) +1
        = ;     =3D 4 – 4 – 3
        = ;     =3D -3
------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0065.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Notation and Algebra of Functions
Notation and Algebra of Functions
Expression can be made = using functions notations.        = ;   
Examp= le:  Let f(x) =3D x2 – 2x – 3, g(x) =3D 2x + 1.
a.Simplify f(2) – g(-3)&= #13;
      f<= span lang=3DEN-US style=3D'color:red;mso-fareast-language:ZH-CN'>(2) =3D (2)2 – 2*(2) R= 11; 3     g= (-3) =3D 2(-3) +1
        = ;     =3D 4 – 4 – 3        = ;            &n= bsp;  =3D -6 + 1
        = ;     =3D -3        = ;            &n= bsp;             =3D -5
------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0066.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Notation and Algebra of Functions
Notation and Algebra of Functions
Expression= can be made using functions notations.        = ;   
Example:  Let f(x) =3D x2 – 2x – 3, g(x) =3D 2x + 1.
<= span style=3D'color:#009999;mso-color-index:6'>a.Simpl= ify f(2) – g(-3)
      f<= span lang=3DEN-US style=3D'color:red;mso-fareast-language:ZH-CN'>(2) =3D (2)2 – 2*(2) R= 11; 3     g= (-3) =3D 2(-3) +1
        = ;     =3D 4 – 4 – 3        = ;            &n= bsp;  =3D -6 + 1
        = ;     =3D -3        = ;            &n= bsp;             =3D -5
     Hence f(2) R= 11; g(-3)
        = ;       =3D
------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0067.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Notation and Algebra of Functions
Notation and Algebra of Functions
Expression= can be made using functions notations.        = ;   
Example:  Let f(x) =3D x2 – 2x – 3, g(x) =3D 2x + 1.
<= span style=3D'color:#009999;mso-color-index:6'>a.Simpl= ify f(2) – g(-3)
      f<= span lang=3DEN-US style=3D'color:red;mso-fareast-language:ZH-CN'>(2) =3D (2)2 – 2*(2) R= 11; 3     g= (-3) =3D 2(-3) +1
        = ;     =3D 4 – 4 – 3        = ;            &n= bsp;  =3D -6 + 1
        = ;     =3D -3        = ;            &n= bsp;             =3D -5
     Hence f(2) R= 11; g(-3)
        = ;       =3D -3 – (-5)
------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0068.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Notation and Algebra of Functions
Notation and Algebra of Functions
Expression= can be made using functions notations.        = ;   
Example:  Let f(x) =3D x2 – 2x – 3, g(x) =3D 2x + 1.
<= span style=3D'color:#009999;mso-color-index:6'>a.Simpl= ify f(2) – g(-3)
      f<= span lang=3DEN-US style=3D'color:red;mso-fareast-language:ZH-CN'>(2) =3D (2)2 – 2*(2) R= 11; 3     g= (-3) =3D 2(-3) +1
        = ;     =3D 4 – 4 – 3        = ;            &n= bsp;  =3D -6 + 1
        = ;     =3D -3        = ;            &n= bsp;             =3D -5
     Hence f(2) R= 11; g(-3)
        = ;       =3D -3 – (-5) =3D -3 + 5 =3D 2
------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0068_image021.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhHAAlAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAAAc ACUAgAAAAAAAAAJNjI+pG+APo4xm2usq3lBz7n1YKFpkKZ1o16xm66ZwzNKyTc24GvOuvwKihCWi yPhBgnQ25cY5YtKgF+oLV8NmpD3uzxsED8VFAOOMLgAAOw== ------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0069.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Notation and Algebra of Functions
Notation and Algebra of Functions
Expression can be made = using functions notations.        = ;   
Examp= le:  Let f(x) =3D x2 – 2x – 3, g(x) =3D 2x + 1.
b.    Simplify f(x + h ) &#= 8211; f(x)
------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0070.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Notation and Algebra of Functions
Notation and Algebra of Functions
Expression can be made = using functions notations.        = ;   
Examp= le:  Let f(x) =3D x2 – 2x – 3, g(x) =3D 2x + 1.
b.    Simplify f(x + h ) &#= 8211; f(x)
f(x + h )= =3D (x+h)2 – 2(x+h) R= 11; 3
        = ;    
------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0071.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Notation and Algebra of Functions
Notation and Algebra of Functions
Expression can be made = using functions notations.        = ;   
Examp= le:  Let f(x) =3D x2 – 2x – 3, g(x) =3D 2x + 1.
b.    Simplify f(x + h ) &#= 8211; f(x)
f(x += h ) =3D (= x+h)2 – 2(x+h) – 3
        = ;     =3D x2 + 2xh + h2 – 2x – 2h – 3  = ;
------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0072.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Notation and Algebra of Functions
Notation and Algebra of Functions
Expression can be made = using functions notations.        = ;   
Examp= le:  Let f(x) =3D x2 – 2x – 3, g(x) =3D 2x + 1.
b.    Simplify f(x + h ) &#= 8211; f(x)
f(x += h ) =3D (x+h)2 – 2(x+h) – 3
        = ;     =3D x2 = + 2xh + h2 – 2x – 2h – 3&nb= sp;
Hence f(x+h) – = f(x)
     =3D =
------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0073.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Notation and Algebra of Functions
Notation and Algebra of Functions
Expression can be made = using functions notations.        = ;   
Examp= le:  Let f(x) =3D x2 – 2x – 3, g(x) =3D 2x + 1.
b.    Simplify f(x + h ) &#= 8211; f(x)
f(x += h ) =3D (x+h)2 – 2(x+h) – 3
        = ;     =3D x2 = + 2xh + h2 – 2x – 2h – 3&nb= sp;
Hence f(x+h) – = f(x)
     =3D x2 + 2xh + h2 – 2x – 2h – 3 – (x2 – 2x – 3)
    
------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0074.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Notation and Algebra of Functions
Notation and Algebra of Functions
Expression can be made = using functions notations.        = ;   
Examp= le:  Let f(x) =3D x2 – 2x – 3, g(x) =3D 2x + 1.
b.    Simplify f(x + h ) &#= 8211; f(x)
f(x += h ) =3D (x+h)2 – 2(x+h) – 3
        = ;     =3D x2 = + 2xh + h2 – 2x – 2h – 3&nb= sp;
Hence f(x+h) – = f(x)
     =3D x2 + 2xh + h2 – 2x – 2h – 3 – (x2 – 2x – 3)
     =3D x2 + 2xh + h2 – 2x – 2h – 3 – x2 + 2x + 3
------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0075.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Notation and Algebra of Functions
Notation and Algebra of Functions
Expression can be made = using functions notations.        = ;   
Examp= le:  Let f(x) =3D x2 – 2x – 3, g(x) =3D 2x + 1.
b.    Simplify f(x + h ) &#= 8211; f(x)
f(x += h ) =3D (x+h)2 – 2(x+h) – 3
        = ;     =3D x2 = + 2xh + h2 – 2x – 2h – 3&nb= sp;
Hence f(x+h) – = f(x)
     =3D x2 + 2xh + h2 – 2x – 2h – 3 – (x2 – 2x – 3)
     =3D x2 + 2xh + h2 – 2x – 2h – 3 – x2 + 2x + 3
------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0075_image022.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhHgAeAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAc ABwAgAAAAAAAAAI7hI+pGetvgoT0yFbpzXryt31OKCpkiZxo5K1W6wLqOqN1eYv5t3N99qsEO5iY DOYaQpQgJM1pg9KMiAIAOw== ------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0075_image023.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhHgAiAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAc ACAAgAAAAAAAAAJChI+pGLEPTXOxymbtzHVz6H1LKCZkyVCoia2p6gLnOqN1eeNwnH8998sENa2Y rGhE8pQ0ps2p2zWlT+rTeBgKsYcCADs= ------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0075_image024.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhHgAeAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAc ABwAgAAAAP8AAAI7hI+pGetvgoT0yFbpzXryt31OKCpkiZxo5K1W6wLqOqN1eYv5t3N99qsEO5iY DOYaQpQgJM1pg9KMiAIAOw== ------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0075_image025.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhHgAiAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAc ACAAgAAAAP8AAAJChI+pGetvgoT0yFbpzXryt32gJyphyZCopa7A6b7tCsc1PaO3npe73xP9gDHE 8HPkJDPLSrODKcqkkSDSqsRmqYYCADs= ------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0075_image026.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQAaAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAX ABcAgAAAAJnMAAIuhI+poe0BnTSQzRdvq3rnjnBg+I2AaJ7liJotu4KvHHezXWu3nl+735v8gClE AQA7 ------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0075_image027.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhFQAaAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAT ABgAgAAAAJnMAAIshI9poY0BnYtSQVYfzWvzy2nhAY5leH6eOnYYulZpNtOxVOP3tDe5/jK1DAUA Ow== ------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0076.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Notation and Algebra of Functions
Notation and Algebra of Functions
Expression can be made = using functions notations.        = ;   
Examp= le:  Let f(x) =3D x2 – 2x – 3, g(x) =3D 2x + 1.
b.    Simplify f(x + h ) &#= 8211; f(x)
f(x += h ) =3D (x+h)2 – 2(x+h) – 3
        = ;     =3D x2 = + 2xh + h2 – 2x – 2h – 3&nb= sp;
Hence f(x+h) – = f(x)
     =3D x2 + 2xh + h2 – 2x – 2h – 3 – (x2 – 2x – 3)
     =3D x2 + 2xh + h2 – 2x – 2h – 3 – x2 + 2x + 3
     =3D2xh + h2 – 2h 
------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0076_image028.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhHgAeAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAc ABwAgAAAAAAAAAI7hI+pGetvgoT0yFbpzXryt31OKCpkiZxo5K1W6wLqOqN1eYv5t3N99qsEO5iY DOYaQpQgJM1pg9KMiAIAOw== ------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0076_image029.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhHgAiAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAc ACAAgAAAAAAAAAJChI+pGLEPTXOxymbtzHVz6H1LKCZkyVCoia2p6gLnOqN1eeNwnH8998sENa2Y rGhE8pQ0ps2p2zWlT+rTeBgKsYcCADs= ------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0076_image030.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhHgAeAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAc ABwAgAAAAP8AAAI7hI+pGetvgoT0yFbpzXryt31OKCpkiZxo5K1W6wLqOqN1eYv5t3N99qsEO5iY DOYaQpQgJM1pg9KMiAIAOw== ------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0076_image031.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhHgAiAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAc ACAAgAAAAP8AAAJChI+pGetvgoT0yFbpzXryt32gJyphyZCopa7A6b7tCsc1PaO3npe73xP9gDHE 8HPkJDPLSrODKcqkkSDSqsRmqYYCADs= ------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0076_image032.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQAaAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAX ABcAgAAAAJnMAAIuhI+poe0BnTSQzRdvq3rnjnBg+I2AaJ7liJotu4KvHHezXWu3nl+735v8gClE AQA7 ------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0076_image033.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhFQAaAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAT ABgAgAAAAJnMAAIshI9poY0BnYtSQVYfzWvzy2nhAY5leH6eOnYYulZpNtOxVOP3tDe5/jK1DAUA Ow== ------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0076_image034.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhpgAhAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAACm ACAAgAAAAAAAAAKPjI+py+0Po5y0QhCA3rz7D4biSJbmiaajobbuC8dyys72jed4rff+D9TwgsSi 8TQ8KpfKJPMJ1Tmj1Kpras1qRdit99v9iq3hsflZPquN6bX7137Ld5m5nRi/61v5vd/U9ycYEjho yFF4eJioOMjY+PcIuSc5eVdpOYeZ+bbJueb5eRYqOmZxipqqusqKWgAAOw== ------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0096.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Notation and Algebra of Functions
Notation and Algebra of Functions
f (X) =3D X2 – 2X + 3=
------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0097.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Notation and Algebra of Functions
Notation and Algebra of Functions
f (X) =3D X2 – 2X + 3=
One basic question of any function is its domain, i.e. what number= s may be used for x to evaluate with this formula f?
=
------=_NextPart_01C82DF7.23E03F50 Content-Location: file:///C:/4D764A33/1NotationandAlgebraofFunctions_files/slide0098.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Notation and Algebra of Functions
Notation and Algebra of Functions
f (X) =3D X2 – 2X + 3=