Sign Charts and Inequlities

Sign-Charts and Inequalities

Some important questions about any given formula f are:

•<= /span>

= 3;

Sign-Charts and Inequalities

Some important questions about any given formula f are:

• when will the formula= f output 0 (f=3D0)

= 3;

Sign -Charts and Inequalities

Some important questions about any given formula f are:

• when will the formula f output 0 (f=3D0)

• when will it output positive quantities (f>0)

&nbs= p;

Sign-Charts and Inequalities

Some important questions= about any given formula f are:

• when will the formula f output 0 (f=3D0)

• when will it output positive quantities (f>0)

• when will it output negative quant= ities (f<0)

= 3;

Sign-Charts and Inequalities

Some important questions= about any given formula f are:

• when will the formula f output 0 (f=3D0)

• when will it output positive quantities (f>0)

• when will it output negative quant= ities (f<0)

We = use sign-charts to answer them.

= 3;

Sign-Charts and Inequalities

Example: Let f =3D x + 5, use the sign chart to

indicate when is f =3D 0, f > 0, and f < 0?

Sign-Charts and Inequalities

Example: Let f =3D x + 5, use the sign chart to

indicate when is f =3D 0, f > 0, and f < 0?

To construct the sign-chart of f:

Sign-Charts and Inequalities

Example: Let f =3D x + 5, use the sign chart to

indicate when is f =3D 0, f > 0, and f < 0?

To construct the sign-= chart of = f:

I. Solve for f =3D 0, = and

denominator =3D 0 if t= here is any denominator.

Sign-Charts and Inequalities

Example: Let f =3D x + 5, use the sign chart to

indicate when is f =3D 0, f > 0, and f < 0?

To construct the sign-= chart of = f:

I. Solve for f =3D 0, = and

denominator =3D 0 if t= here is any denominator.

II. Draw the real line <= /span>and mark = off the answers f= rom I.

Sign-Charts and Inequalities

Example: Let f =3D x + 5, use the sign chart to

indicate when is f =3D 0, f > 0, and f < 0?

To construct the sign-= chart of = f:

I. Solve for f =3D 0, = and

denominator =3D 0 if t= here is any denominator.

II. Draw the real line <= /span>and mark = off the answers f= rom I.

III. Sample each segment f= or signs by testing a point in each segment.

Sign-Charts and Inequalities

Example: Let f =3D x + 5, use the sign chart to

indicate when is f =3D 0, f > 0, and f < 0?

To construct the sign-= chart of = f:

I. Solve for f =3D 0, = and

denominator =3D 0 if t= here is any denominator.

II. Draw the real line <= /span>and mark = off the answers f= rom I.

III. Sample each segment f= or signs by testing a point in each segment.

Solve x + 5 =3D 0 à= ; x =3D -5

Sign-Charts and Inequalities

Example: Let f =3D x + 5, use the sign chart to

indicate when is f =3D 0, f > 0, and f < 0?

To construct the sign-= chart of = f:

I. Solve for f =3D 0, = and

denominator =3D 0 if t= here is any denominator.

II. Draw the real line <= /span>and mark = off the answers f= rom I.

III. Sample each segment f= or signs by testing a point in each segment.

Solve x + 5 =3D 0 à x =3D -5 =

Draw a line, mark off x =3D -5

Sign-Charts and Inequalities

Example: Let f =3D x + 5, use the sign chart to

indicate when is f =3D 0, f > 0, and f < 0?

To construct the sign-= chart of = f:

I. Solve for f =3D 0, = and

denominator =3D 0 if t= here is any denominator.

II. Draw the real line <= /span>and mark = off the answers f= rom I.

III. Sample each segment f= or signs by testing a point in each segment.

Solve x + 5 =3D 0 à= ; x =3D -5

Draw a line, mark off x =3D -5:

0

-5

Sign-Charts and Inequalities

Example: Let f =3D x + 5, use the sign chart to

indicate when is f =3D 0, f > 0, and f < 0?

To construct the sign-= chart of = f:

I. Solve for f =3D 0, = and

denominator =3D 0 if t= here is any denominator.

II. Draw the real line <= /span>and mark = off the answers f= rom I.

III. Sample each segment f= or signs by testing a point in each segment.

Solve x + 5 =3D 0 à= ; x =3D -5

Draw a line, mark off x =3D -5:

0

-5

test x =3D 0,

Sign-Charts and Inequalities

Example: Let f =3D x + 5, use the sign chart to

indicate when is f =3D 0, f > 0, and f < 0?

To construct the sign-= chart of = f:

I. Solve for f =3D 0, = and

denominator =3D 0 if t= here is any denominator.

II. Draw the real line <= /span>and mark = off the answers f= rom I.

III. Sample each segment f= or signs by testing a point in each segment.

Solve x + 5 =3D 0 à= ; x =3D -5

Draw a line, mark off x =3D -5:

0

-5

test x =3D 0, 0+5 =3D 5 is positive.

Sign-Charts and Inequalities

Example: Let f =3D x + 5, use the sign chart to

indicate when is f =3D 0, f > 0, and f < 0?

To construct the sign-= chart of = f:

I. Solve for f =3D 0, = and

denominator =3D 0 if t= here is any denominator.

II. Draw the real line <= /span>and mark = off the answers f= rom I.

III. Sample each segment f= or signs by testing a point in each segment.

Solve x + 5 =3D 0 à= ; x =3D -5

Draw a line, mark off x =3D -5:

0

-5

test x =3D 0, 0+5 =3D 5 is positive. Hence that =

segment is a positive segme= nt.

Sign-Charts and Inequalities

Example: Let f =3D x + 5, use the sign chart to

indicate when is f =3D 0, f > 0, and f < 0?

To construct the sign-= chart of = f:

I. Solve for f =3D 0, = and

denominator =3D 0 if t= here is any denominator.

II. Draw the real line <= /span>and mark = off the answers f= rom I.

III. Sample each segment f= or signs by testing a point in each segment.

Solve x + 5 =3D 0 à= ; x =3D -5

Draw a line, mark off x =3D -5:

+ + + + + + + + + +

0

-5

test x =3D 0, 0+5 =3D 5 is positive.&n= bsp; Hence that

segment is a positive segment.

------=_NextPart_01C82DF5.B3A6A720 Content-Location: file:///C:/1ECBB113/6SignChartsandInequlities_files/slide0024_image013.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCQECAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAH AQEAgAAAAAAAAAIOjI+py+0Po5y02ouzdgUAOw== ------=_NextPart_01C82DF5.B3A6A720 Content-Location: file:///C:/1ECBB113/6SignChartsandInequlities_files/slide0024_image014.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAK AAoAgQAAAAAAAP8AAAECAwIYhINhF+KiznuqTVcvtTfryFELgkULgJwFADs= ------=_NextPart_01C82DF5.B3A6A720 Content-Location: file:///C:/1ECBB113/6SignChartsandInequlities_files/slide0024_image015.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhAgALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAB AAkAgAAAAAAAAAIDjH8FADs= ------=_NextPart_01C82DF5.B3A6A720 Content-Location: file:///C:/1ECBB113/6SignChartsandInequlities_files/slide0024_image016.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhAgALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAB AAkAgAAAAAAAAAIDjH8FADs= ------=_NextPart_01C82DF5.B3A6A720 Content-Location: file:///C:/1ECBB113/6SignChartsandInequlities_files/slide0087.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Sign Charts and Inequlities

Sign-Charts and Inequalities

Example: Let f =3D x + 5, use the sign chart to

indicate when is f =3D 0, f > 0, and f < 0?

To construct the sign-= chart of = f:

I. Solve for f =3D 0, = and

denominator =3D 0 if t= here is any denominator.

II. Draw the real line <= /span>and mark = off the answers f= rom I.

III. Sample each segment f= or signs by testing a point in each segment.

Solve x + 5 =3D 0 à= ; x =3D -5

Draw a line, mark off x =3D -5:

+ + + + + + + + + +

0

-5

test x =3D 0, 0+5 =3D 5 is positive.&n= bsp; Hence that

segment is a positive segment.

test x =3D -6,

------=_NextPart_01C82DF5.B3A6A720 Content-Location: file:///C:/1ECBB113/6SignChartsandInequlities_files/slide0087_image017.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCQECAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAH AQEAgAAAAAAAAAIOjI+py+0Po5y02ouzdgUAOw== ------=_NextPart_01C82DF5.B3A6A720 Content-Location: file:///C:/1ECBB113/6SignChartsandInequlities_files/slide0087_image018.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAK AAoAgQAAAAAAAP8AAAECAwIYhINhF+KiznuqTVcvtTfryFELgkULgJwFADs= ------=_NextPart_01C82DF5.B3A6A720 Content-Location: file:///C:/1ECBB113/6SignChartsandInequlities_files/slide0087_image019.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhAgALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAB AAkAgAAAAAAAAAIDjH8FADs= ------=_NextPart_01C82DF5.B3A6A720 Content-Location: file:///C:/1ECBB113/6SignChartsandInequlities_files/slide0087_image020.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhAgALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAB AAkAgAAAAAAAAAIDjH8FADs= ------=_NextPart_01C82DF5.B3A6A720 Content-Location: file:///C:/1ECBB113/6SignChartsandInequlities_files/slide0025.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Sign Charts and Inequlities

Sign-Charts and Inequalities

Example: Let f =3D x + 5, use the sign chart to

indicate when is f =3D 0, f > 0, and f < 0?

To construct the sign-= chart of = f:

I. Solve for f =3D 0, = and

denominator =3D 0 if t= here is any denominator.

II. Draw the real line <= /span>and mark = off the answers f= rom I.

III. Sample each segment f= or signs by testing a point in each segment.

Solve x + 5 =3D 0 à= ; x =3D -5

Draw a line, mark off x =3D -5:

+ + + + + + + + + +

0

-5

test x =3D 0, 0+5 =3D 5 is positive.&n= bsp; Hence that

segment is a positive segment.

test x =3D -6,

5+(-6) =3D -1 is

negative,

------=_NextPart_01C82DF5.B3A6A720 Content-Location: file:///C:/1ECBB113/6SignChartsandInequlities_files/slide0025_image021.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCQECAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAH AQEAgAAAAAAAAAIOjI+py+0Po5y02ouzdgUAOw== ------=_NextPart_01C82DF5.B3A6A720 Content-Location: file:///C:/1ECBB113/6SignChartsandInequlities_files/slide0025_image022.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAK AAoAgQAAAAAAAP8AAAECAwIYhINhF+KiznuqTVcvtTfryFELgkULgJwFADs= ------=_NextPart_01C82DF5.B3A6A720 Content-Location: file:///C:/1ECBB113/6SignChartsandInequlities_files/slide0025_image023.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhAgALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAB AAkAgAAAAAAAAAIDjH8FADs= ------=_NextPart_01C82DF5.B3A6A720 Content-Location: file:///C:/1ECBB113/6SignChartsandInequlities_files/slide0025_image024.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhAgALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAB AAkAgAAAAAAAAAIDjH8FADs= ------=_NextPart_01C82DF5.B3A6A720 Content-Location: file:///C:/1ECBB113/6SignChartsandInequlities_files/slide0026.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Sign Charts and Inequlities

Sign-Charts and Inequalities

Example: Let f =3D x + 5, use the sign chart to

indicate when is f =3D 0, f > 0, and f < 0?

To construct the sign-= chart of = f:

I. Solve for f =3D 0, = and

denominator =3D 0 if t= here is any denominator.

II. Draw the real line <= /span>and mark = off the answers f= rom I.

III. Sample each segment f= or signs by testing a point in each segment.

Solve x + 5 =3D 0 à= ; x =3D -5

Draw a line, mark off x =3D -5:

- - - - - - + + + + + + + + + +

0

-5

test x =3D 0, 0+5 =3D 5 is positive.&n= bsp; Hence that

segment is a positive segment.

test x =3D -6,

5+(-6) =3D -1 is

negative, so

This segment is negative.

-6

------=_NextPart_01C82DF5.B3A6A720 Content-Location: file:///C:/1ECBB113/6SignChartsandInequlities_files/slide0026_image025.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCQECAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAH AQEAgAAAAAAAAAIOjI+py+0Po5y02ouzdgUAOw== ------=_NextPart_01C82DF5.B3A6A720 Content-Location: file:///C:/1ECBB113/6SignChartsandInequlities_files/slide0026_image026.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAK AAoAgQAAAAAAAP8AAAECAwIYhINhG+KCznuqTWovzLdqCHCOcljRUqIFADs= ------=_NextPart_01C82DF5.B3A6A720 Content-Location: file:///C:/1ECBB113/6SignChartsandInequlities_files/slide0026_image027.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhAgALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAB AAkAgAAAAAAAAAIDjH8FADs= ------=_NextPart_01C82DF5.B3A6A720 Content-Location: file:///C:/1ECBB113/6SignChartsandInequlities_files/slide0026_image028.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhAgALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAB AAoAgAAAAAAAAAIDjI8FADs= ------=_NextPart_01C82DF5.B3A6A720 Content-Location: file:///C:/1ECBB113/6SignChartsandInequlities_files/slide0010.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Sign Charts and Inequlities

Sign-Charts and Inequalities

Example: Let f =3D x2 – 3x – 4 , use the sign-

chart to indicate when is f =3D 0, f > 0, a= nd f < 0.

------=_NextPart_01C82DF5.B3A6A720 Content-Location: file:///C:/1ECBB113/6SignChartsandInequlities_files/slide0027.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Sign Charts and Inequlities

Sign-Charts and Inequalities

Example: Let f =3D x2 – 3x – 4 , use the sign-

chart to indicate when is f =3D 0, f > 0, a= nd f < 0.

Solve x2 – 3x = 211; 4 =3D 0

------=_NextPart_01C82DF5.B3A6A720 Content-Location: file:///C:/1ECBB113/6SignChartsandInequlities_files/slide0028.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Sign Charts and Inequlities

Sign-Charts and Inequalities

Example: Let f =3D x2 – 3x – 4 , use the sign-

chart to indicate when is f =3D 0, f > 0, a= nd f < 0.

Solve x2 – 3x = 211; 4 =3D 0

(x – 4)(x + 1) =3D 0 à= ; x =3D 4 , -1

------=_NextPart_01C82DF5.B3A6A720 Content-Location: file:///C:/1ECBB113/6SignChartsandInequlities_files/slide0029.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Sign Charts and Inequlities

Sign-Charts and Inequalities

Example: Let f =3D x2 – 3x – 4 , use the sign-

chart to indicate when is f =3D 0, f > 0, a= nd f < 0.

Solve x2 – 3x = 211; 4 =3D 0

(x – 4)(x + 1) =3D 0 à= ; x =3D 4 , -1

Mark off these points on a line:

------=_NextPart_01C82DF5.B3A6A720 Content-Location: file:///C:/1ECBB113/6SignChartsandInequlities_files/slide0030.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Sign Charts and Inequlities

Sign-Charts and Inequalities

Example: Let f =3D x2 – 3x – 4 , use the sign-

chart to indicate when is f =3D 0, f > 0, a= nd f < 0.

Solve x2 – 3x = 211; 4 =3D 0

(x – 4)(x + 1) =3D 0 à= ; x =3D 4 , -1

Mark off these points on a line:

(x-4)(x+1)

0

4

-1

------=_NextPart_01C82DF5.B3A6A720 Content-Location: file:///C:/1ECBB113/6SignChartsandInequlities_files/slide0030_image029.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhigECAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAACI AQEAgAAAAAAAAAIRjI+py+0Po5y02ouz3rz7LxUAOx== ------=_NextPart_01C82DF5.B3A6A720 Content-Location: file:///C:/1ECBB113/6SignChartsandInequlities_files/slide0030_image030.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhAgALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAB AAoAgAAAAAAAAAIDjI8FADs= ------=_NextPart_01C82DF5.B3A6A720 Content-Location: file:///C:/1ECBB113/6SignChartsandInequlities_files/slide0030_image031.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAK AAoAgQAAAAAAAP8AAAECAwIXhINhG+KCznuqTWovzBdpV2nKYUULeRYAOx== ------=_NextPart_01C82DF5.B3A6A720 Content-Location: file:///C:/1ECBB113/6SignChartsandInequlities_files/slide0030_image032.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAJ AAoAgQAAAAAAAP8AAAECAwIWBIJoJ93BnENyhvoupjtOwwnQcihGAQA7 ------=_NextPart_01C82DF5.B3A6A720 Content-Location: file:///C:/1ECBB113/6SignChartsandInequlities_files/slide0031.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Sign Charts and Inequlities

Sign-Charts and Inequalities

Example: Let f =3D x2 – 3x – 4 , use the sign-

chart to indicate when is f =3D 0, f > 0, a= nd f < 0.

Solve x2 – 3x = 211; 4 =3D 0

(x – 4)(x + 1) =3D 0 à= ; x =3D 4 , -1

Mark off these points on a line:

(x-4)(x+1)

0

4

-1

Select points to sample in each segment: =

------=_NextPart_01C82DF5.B3A6A720 Content-Location: file:///C:/1ECBB113/6SignChartsandInequlities_files/slide0031_image033.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhkwECAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAACR AQEAgAAAAAAAAAIRjI+py+0Po5y02ouz3rz7vxUAOx== ------=_NextPart_01C82DF5.B3A6A720 Content-Location: file:///C:/1ECBB113/6SignChartsandInequlities_files/slide0031_image034.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhAgALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAB AAoAgAAAAAAAAAIDjI8FADs= ------=_NextPart_01C82DF5.B3A6A720 Content-Location: file:///C:/1ECBB113/6SignChartsandInequlities_files/slide0031_image035.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAK AAoAgQAAAAAAAP8AAAECAwIXhINhG+KCznuqTWovzBdpV2nKYUULeRYAOx== ------=_NextPart_01C82DF5.B3A6A720 Content-Location: file:///C:/1ECBB113/6SignChartsandInequlities_files/slide0031_image036.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAJ AAoAgQAAAAAAAP8AAAECAwIWBIJoJ93BnENyhvoupjtOwwnQcihGAQA7 ------=_NextPart_01C82DF5.B3A6A720 Content-Location: file:///C:/1ECBB113/6SignChartsandInequlities_files/slide0032.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Sign Charts and Inequlities

Sign-Charts and Inequalities

Example: Let f =3D x2 – 3x – 4 , use the sign-

chart to indicate when is f =3D 0, f > 0, a= nd f < 0.

Solve x2 – 3x = 211; 4 =3D 0

(x – 4)(x + 1) =3D 0 à= ; x =3D 4 , -1

Mark off these points on a line:

(x-4)(x+1)

0

4

-1

Select points to sample in each segment:

Test x =3D - 2.=

-2

------=_NextPart_01C82DF5.B3A6A720 Content-Location: file:///C:/1ECBB113/6SignChartsandInequlities_files/slide0032_image037.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhkwECAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAACR AQEAgAAAAAAAAAIRjI+py+0Po5y02ouz3rz7vxUAOx== ------=_NextPart_01C82DF5.B3A6A720 Content-Location: file:///C:/1ECBB113/6SignChartsandInequlities_files/slide0032_image038.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhAgALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAB AAoAgAAAAAAAAAIDjI8FADs= ------=_NextPart_01C82DF5.B3A6A720 Content-Location: file:///C:/1ECBB113/6SignChartsandInequlities_files/slide0032_image039.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAK AAoAgQAAAAAAAP8AAAECAwIXhINhG+KCznuqTWovzBdpV2nKYUULeRYAOx== ------=_NextPart_01C82DF5.B3A6A720 Content-Location: file:///C:/1ECBB113/6SignChartsandInequlities_files/slide0032_image040.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAJ AAoAgQAAAAAAAP8AAAECAwIWBIJoJ93BnENyhvoupjtOwwnQcihGAQA7 ------=_NextPart_01C82DF5.B3A6A720 Content-Location: file:///C:/1ECBB113/6SignChartsandInequlities_files/slide0032_image041.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhBwALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAF AAoAgQAAAAAAAJkzAAECAwINjC9pKavBXIMv0nlCAQA7 ------=_NextPart_01C82DF5.B3A6A720 Content-Location: file:///C:/1ECBB113/6SignChartsandInequlities_files/slide0032_image042.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhAwAEAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAB AAIAgAAAAAAAAAICTAoAOw== ------=_NextPart_01C82DF5.B3A6A720 Content-Location: file:///C:/1ECBB113/6SignChartsandInequlities_files/slide0033.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Sign Charts and Inequlities

Sign-Charts and Inequalities

Example: Let f =3D x2 – 3x – 4 , use the sign-

chart to indicate when is f =3D 0, f > 0, a= nd f < 0.

Solve x2 – 3x = 211; 4 =3D 0

(x – 4)(x + 1) =3D 0 à= ; x =3D 4 , -1

Mark off these points on a line:

(x-4)(x+1)

0

4

-1

Select points to sample in each segment:

Test x =3D - 2.=

Get – * – =3D = + .

-2

------=_NextPart_01C82DF5.B3A6A720 Content-Location: file:///C:/1ECBB113/6SignChartsandInequlities_files/slide0033_image043.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhkwECAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAACR AQEAgAAAAAAAAAIRjI+py+0Po5y02ouz3rz7vxUAOx== ------=_NextPart_01C82DF5.B3A6A720 Content-Location: file:///C:/1ECBB113/6SignChartsandInequlities_files/slide0033_image044.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhAgALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAB AAoAgAAAAAAAAAIDjI8FADs= ------=_NextPart_01C82DF5.B3A6A720 Content-Location: file:///C:/1ECBB113/6SignChartsandInequlities_files/slide0033_image045.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAK AAoAgQAAAAAAAP8AAAECAwIXhINhG+KCznuqTWovzBdpV2nKYUULeRYAOx== ------=_NextPart_01C82DF5.B3A6A720 Content-Location: file:///C:/1ECBB113/6SignChartsandInequlities_files/slide0033_image046.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAJ AAoAgQAAAAAAAP8AAAECAwIWBIJoJ93BnENyhvoupjtOwwnQcihGAQA7 ------=_NextPart_01C82DF5.B3A6A720 Content-Location: file:///C:/1ECBB113/6SignChartsandInequlities_files/slide0033_image047.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhBwALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAF AAoAgQAAAAAAAJkzAAECAwINjC9pKavBXIMv0nlCAQA7 ------=_NextPart_01C82DF5.B3A6A720 Content-Location: file:///C:/1ECBB113/6SignChartsandInequlities_files/slide0034.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Sign Charts and Inequlities

Sign-Charts and Inequalities

Example: Let f =3D x2 – 3x – 4 , use the sign-

chart to indicate when is f =3D 0, f > 0, a= nd f < 0.

Solve x2 – 3x = 211; 4 =3D 0

(x – 4)(x + 1) =3D 0 à= ; x =3D 4 , -1

Mark off these points on a line:

(x-4)(x+1) =

0

4

-1

Select points to sample in each segment:

Test x =3D - 2.=

Get – * – =3D = + .

Hence the segme= nt

is positive. Draw +

sign over it. &= #13;

-2

------=_NextPart_01C82DF5.B3A6A720 Content-Location: file:///C:/1ECBB113/6SignChartsandInequlities_files/slide0034_image048.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhkwECAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAACR AQEAgAAAAAAAAAIRjI+py+0Po5y02ouz3rz7vxUAOx== ------=_NextPart_01C82DF5.B3A6A720 Content-Location: file:///C:/1ECBB113/6SignChartsandInequlities_files/slide0034_image049.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhAgALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAB AAoAgAAAAAAAAAIDjI8FADs= ------=_NextPart_01C82DF5.B3A6A720 Content-Location: file:///C:/1ECBB113/6SignChartsandInequlities_files/slide0034_image050.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAK AAoAgQAAAAAAAP8AAAECAwIXhINhG+KCznuqTWovzBdpV2nKYUULeRYAOx== ------=_NextPart_01C82DF5.B3A6A720 Content-Location: file:///C:/1ECBB113/6SignChartsandInequlities_files/slide0034_image051.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAJ AAoAgQAAAAAAAP8AAAECAwIWBIJoJ93BnENyhvoupjtOwwnQcihGAQA7 ------=_NextPart_01C82DF5.B3A6A720 Content-Location: file:///C:/1ECBB113/6SignChartsandInequlities_files/slide0034_image052.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhBwALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAF AAoAgQAAAAAAAJkzAAECAwINjC9pKavBXIMv0nlCAQA7 ------=_NextPart_01C82DF5.B3A6A720 Content-Location: file:///C:/1ECBB113/6SignChartsandInequlities_files/slide0036.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Sign Charts and Inequlities

Sign-Charts and Inequalities

Example: Let f =3D x2 – 3x – 4 , use the sign-

chart to indicate when is f =3D 0, f > 0, a= nd f < 0.

Solve x2 – 3x = 211; 4 =3D 0

(x – 4)(x + 1) =3D 0 à= ; x =3D 4 , -1

Mark off these points on a line:

(x-4)(x+1) + + + + + + + + +

0

4

-1

Select points to sample in each segment:

Test x =3D - 2.=

Get – * – =3D = + .

Hence the segme= nt

is positive. Draw +

sign over it. &= #13;

-2

------=_NextPart_01C82DF5.B3A6A720 Content-Location: file:///C:/1ECBB113/6SignChartsandInequlities_files/slide0036_image053.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhkwECAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAACR AQEAgAAAAAAAAAIRjI+py+0Po5y02ouz3rz7vxUAOx== ------=_NextPart_01C82DF5.B3A6A720 Content-Location: file:///C:/1ECBB113/6SignChartsandInequlities_files/slide0036_image054.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhAgALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAB AAoAgAAAAAAAAAIDjI8FADs= ------=_NextPart_01C82DF5.B3A6A720 Content-Location: file:///C:/1ECBB113/6SignChartsandInequlities_files/slide0036_image055.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAK AAoAgQAAAAAAAP8AAAECAwIXhINhG+KCznuqTWovzBdpV2nKYUULeRYAOx== ------=_NextPart_01C82DF5.B3A6A720 Content-Location: file:///C:/1ECBB113/6SignChartsandInequlities_files/slide0036_image056.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAJ AAoAgQAAAAAAAP8AAAECAwIWBIJoJ93BnENyhvoupjtOwwnQcihGAQA7 ------=_NextPart_01C82DF5.B3A6A720 Content-Location: file:///C:/1ECBB113/6SignChartsandInequlities_files/slide0036_image057.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhBwALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAF AAoAgQAAAAAAAJkzAAECAwINjC9pKavBXIMv0nlCAQA7 ------=_NextPart_01C82DF5.B3A6A720 Content-Location: file:///C:/1ECBB113/6SignChartsandInequlities_files/slide0035.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Sign Charts and Inequlities

Sign-Charts and Inequalities

Example: Let f =3D x2 – 3x – 4 , use the sign-

chart to indicate when is f =3D 0, f > 0, a= nd f < 0.

Solve x2 – 3x = 211; 4 =3D 0

(x – 4)(x + 1) =3D 0 à= ; x =3D 4 , -1

Mark off these points on a line:

(x-4)(x+1) + + + + + + + + +

0

4

-1

Select points to sample in each segment:

Test x =3D - 2,=

Get – * – =3D = + .

Hence the segme= nt

is positive. Draw +

sign over it. &= #13;

-2

Test x =3D 0.

Get&= nbsp; – * + =3D ̵= 1;.

------=_NextPart_01C82DF5.B3A6A720 Content-Location: file:///C:/1ECBB113/6SignChartsandInequlities_files/slide0035_image058.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhkwECAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAACR AQEAgAAAAAAAAAIRjI+py+0Po5y02ouz3rz7vxUAOx== ------=_NextPart_01C82DF5.B3A6A720 Content-Location: file:///C:/1ECBB113/6SignChartsandInequlities_files/slide0035_image059.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhAgALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAB AAoAgAAAAAAAAAIDjI8FADs= ------=_NextPart_01C82DF5.B3A6A720 Content-Location: file:///C:/1ECBB113/6SignChartsandInequlities_files/slide0035_image060.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAK AAoAgQAAAAAAAP8AAAECAwIXhINhG+KCznuqTWovzBdpV2nKYUULeRYAOx== ------=_NextPart_01C82DF5.B3A6A720 Content-Location: file:///C:/1ECBB113/6SignChartsandInequlities_files/slide0035_image061.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAJ AAoAgQAAAAAAAP8AAAECAwIWBIJoJ93BnENyhvoupjtOwwnQcihGAQA7 ------=_NextPart_01C82DF5.B3A6A720 Content-Location: file:///C:/1ECBB113/6SignChartsandInequlities_files/slide0035_image062.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhBwALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAF AAoAgQAAAAAAAJkzAAECAwINjC9pKavBXIMv0nlCAQA7 ------=_NextPart_01C82DF5.B3A6A720 Content-Location: file:///C:/1ECBB113/6SignChartsandInequlities_files/slide0035_image063.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhBwALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAF AAoAgAAAAAAAAAIGjI+py50FADs= ------=_NextPart_01C82DF5.B3A6A720 Content-Location: file:///C:/1ECBB113/6SignChartsandInequlities_files/slide0037.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Sign Charts and Inequlities

Sign-Charts and Inequalities

Example: Let f =3D x2 – 3x – 4 , use the sign-

chart to indicate when is f =3D 0, f > 0, a= nd f < 0.

Solve x2 – 3x = 211; 4 =3D 0

(x – 4)(x + 1) =3D 0 à= ; x =3D 4 , -1

Mark off these points on a line:

(x-4)(x+1) + + + + + + + + +

0

4

-1

Select points to sample in each segment:

Test x =3D - 2,=

Get – * – =3D = + .

Hence the segme= nt

is positive. Draw +

sign over it. &= #13;

-2

Test x =3D 0.

Get&= nbsp; – * + =3D ̵= 1;.

Hence this segment

is negative.

Put&= nbsp; – over it.

------=_NextPart_01C82DF5.B3A6A720 Content-Location: file:///C:/1ECBB113/6SignChartsandInequlities_files/slide0037_image064.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhkwECAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAACR AQEAgAAAAAAAAAIRjI+py+0Po5y02ouz3rz7vxUAOx== ------=_NextPart_01C82DF5.B3A6A720 Content-Location: file:///C:/1ECBB113/6SignChartsandInequlities_files/slide0037_image065.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhAgALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAB AAoAgAAAAAAAAAIDjI8FADs= ------=_NextPart_01C82DF5.B3A6A720 Content-Location: file:///C:/1ECBB113/6SignChartsandInequlities_files/slide0037_image066.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAK AAoAgQAAAAAAAP8AAAECAwIXhINhG+KCznuqTWovzBdpV2nKYUULeRYAOx== ------=_NextPart_01C82DF5.B3A6A720 Content-Location: file:///C:/1ECBB113/6SignChartsandInequlities_files/slide0037_image067.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAJ AAoAgQAAAAAAAP8AAAECAwIWBIJoJ93BnENyhvoupjtOwwnQcihGAQA7 ------=_NextPart_01C82DF5.B3A6A720 Content-Location: file:///C:/1ECBB113/6SignChartsandInequlities_files/slide0037_image068.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhBwALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAF AAoAgQAAAAAAAJkzAAECAwINjC9pKavBXIMv0nlCAQA7 ------=_NextPart_01C82DF5.B3A6A720 Content-Location: file:///C:/1ECBB113/6SignChartsandInequlities_files/slide0037_image069.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhBwALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAF AAoAgAAAAAAAAAIGjI+py50FADs= ------=_NextPart_01C82DF5.B3A6A720 Content-Location: file:///C:/1ECBB113/6SignChartsandInequlities_files/slide0038.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Sign Charts and Inequlities

Sign-Charts and Inequalities

Example: Let f =3D x2 – 3x – 4 , use the sign-

chart to indicate when is f =3D 0, f > 0, a= nd f < 0.

Solve x2 – 3x = 211; 4 =3D 0

(x – 4)(x + 1) =3D 0 à= ; x =3D 4 , -1

Mark off these points on a line:

(x-4)(x+1) + + + + + + + + + - - - - - - - - - -

0

4

-1

Select points to sample in each segment:

Test x =3D - 2,=

Get – * – =3D = + .

Hence the segme= nt

is positive. Draw +

sign over it. &= #13;

-2

Test x =3D 0.

Get&= nbsp; – * + =3D ̵= 1;.

Hence this segment

is negative.

Put&= nbsp; – over it.

------=_NextPart_01C82DF5.B3A6A720 Content-Location: file:///C:/1ECBB113/6SignChartsandInequlities_files/slide0038_image070.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhkwECAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAACR AQEAgAAAAAAAAAIRjI+py+0Po5y02ouz3rz7vxUAOx== ------=_NextPart_01C82DF5.B3A6A720 Content-Location: file:///C:/1ECBB113/6SignChartsandInequlities_files/slide0038_image071.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhAgALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAB AAoAgAAAAAAAAAIDjI8FADs= ------=_NextPart_01C82DF5.B3A6A720 Content-Location: file:///C:/1ECBB113/6SignChartsandInequlities_files/slide0038_image072.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAK AAoAgQAAAAAAAP8AAAECAwIXhINhG+KCznuqTWovzBdpV2nKYUULeRYAOx== ------=_NextPart_01C82DF5.B3A6A720 Content-Location: file:///C:/1ECBB113/6SignChartsandInequlities_files/slide0038_image073.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAJ AAoAgQAAAAAAAP8AAAECAwIWBIJoJ93BnENyhvoupjtOwwnQcihGAQA7 ------=_NextPart_01C82DF5.B3A6A720 Content-Location: file:///C:/1ECBB113/6SignChartsandInequlities_files/slide0038_image074.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhBwALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAF AAoAgQAAAAAAAJkzAAECAwINjC9pKavBXIMv0nlCAQA7 ------=_NextPart_01C82DF5.B3A6A720 Content-Location: file:///C:/1ECBB113/6SignChartsandInequlities_files/slide0038_image075.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhBwALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAF AAoAgAAAAAAAAAIGjI+py50FADs= ------=_NextPart_01C82DF5.B3A6A720 Content-Location: file:///C:/1ECBB113/6SignChartsandInequlities_files/slide0039.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Sign Charts and Inequlities

Sign-Charts and Inequalities

Example: Let f =3D x2 – 3x – 4 , use the sign-

chart to indicate when is f =3D 0, f > 0, a= nd f < 0.

Solve x2 – 3x = 211; 4 =3D 0

(x – 4)(x + 1) =3D 0 à= ; x =3D 4 , -1

Mark off these points on a line:

(x-4)(x+1) + + + + + + + + + - - - - - - - - - -

0

4

-1

Select points to sample in each segment:

Test x =3D - 2,=

Get – * – =3D = + .

Hence the segme= nt

is positive. Draw +

sign over it. &= #13;

-2

Test x =3D 0.

Get&= nbsp; – * + =3D ̵= 1;.

Hence this segment

is negative.

Put&= nbsp; – over it.

Test x =3D 5.

5

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