Rational Functions: Sketching Graphs

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# Rational Functions: Sketching Graphs - PowerPoint PPT Presentation

Example: Sketch the graph of,. Rational Functions: Sketching Graphs . First find the intercepts. To find the x -intercept(s), set f ( x ) = 0 and solve. 3 x + 5 = 0,. 3 x = - 5,. x = - 5/3,. x -intercept: (- 5/3, 0). To find the y -intercept(s), set x = 0 and solve.

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Presentation Transcript

Example: Sketch the graph of,

Rational Functions: Sketching Graphs

First find the intercepts.

To find the x-intercept(s), set f (x) = 0 and solve.

3x + 5 = 0,

3x = - 5,

x = - 5/3,

x-intercept: (- 5/3, 0)

To find the y-intercept(s), set x = 0 and solve.

y-intercept: (0, - 5/2)

Example: Sketch the graph of,

(continued)

Rational Functions: Sketching Graphs

Second, find the asymptotes.

To find the vertical asymptote(s), set the denominator equal to 0 and solve.

vertical asymptote: x = 2

x – 2 = 0,

Since the degrees of the numerator and denominator are the same (see separate slideshow), the horizontal asymptote is:

y = 3/1.

horizontal asymptote: y = 3

Third, plot the intercepts and asymptotes found on the rectangular coordinate plane (click to see on next slide).

Slide 2

Example: Sketch the graph of,

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(continued)

x-intercept: (- 5/3, 0)

y-intercept: (0, - 5/2)

horizontal asymptote: y = 3

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vertical asymptote: x = 2

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Rational Functions: Sketching Graphs

Slide 3

Example: Sketch the graph of,

(continued)

Fourth, graph the function in the standard viewing window by pressing , entering the function, and pressing

.

Y =

ZOOM

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(1) The intercepts check .

(2) There is a solid vertical line where the vertical asymptote is located.

(3) The horizontal asymptote is not shown.

(4) The graph is in two separate parts.

Rational Functions: Sketching Graphs

NOTES:

Slide 4

Example: Sketch the graph of,

(5, 20/3)

(continued)

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Take care to see that the graph passes through the intercepts.

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Also, it is good to show one point that the graph passes through in each region.

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Rational Functions: Sketching Graphs

Fifth, graph the parts shown by the graphing calculator.

Slide 5

Try: Sketch the graph of,

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(3, 13/5)

(- 3, 13/5)

H.A. y = 1

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y-int. (0, - 1)

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V.A. x = - 2

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V.A. x = 2

Rational Functions: Sketching Graphs

Slide 6

Rational Functions: Sketching Graphs

END OF PRESENTATION

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