Rational Functions Wksht

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Math 1113/2804E Precalculus

Worksheet 4

SKETCHING THE GRAPH OF A RATIONAL FUNCTION

Guidelines for Analyzing Graphs of Rational Functions To sketch the graph of a rational function, use the following guidelines: N (x) where N (x) and D(x) are polynomials. Let f (x) = D(x) 1. Simplify f , if possible. 2. Find and plot the y−intercept(s)(if any) by evaluating f (0). 3. Find the zeros of the numerator N (x) (if any) by solving the equation N(x) = 0. Then plot the corresponding x−intercepts. 4. Find the zeros of the denominator (if any) by solving D(x) = 0. Then sketch the corresponding vertical asymptotes. 5. Find a sketch the horizontal asymptotes(if any) by using the rule for finding the horizontal asymptotes. 6. Plot at least one point between and one point beyond each x−intercept and vertical asymptote. 7. Use smooth curves to complete the graph between and beyond the vertical asymptotes. Problem Sketch the graph of the following rational functions:

(a) f (x) =

1 . 3−x

? Domain: ? x-intercept(s): ? y-intercept(s): ? Vertical Asymptotes: ? Horizontal Asymptotes:

(b) g(x) =

x2 . x2 + 9

? Domain: ? x-intercept(s): ? y-intercept(s): ? Vertical Asymptotes: ? Horizontal Asymptotes:

Math 1113/2804E Worksheet 4 February 20, 2008

(c) h(s) =

s . s2 + 1

? Domain: ? x-intercept(s): ? y-intercept(s): ? Vertical Asymptotes: ? Horizontal Asymptotes:

(d) k(x) = −

1 . (x − 2)2

? Domain: ? x-intercept(s): ? y-intercept(s): ? Vertical Asymptotes: ? Horizontal Asymptotes:

(e) r(x) =

x2 − 5x + 4 . x2 − 4

? Domain: ? x-intercept(s): ? y-intercept(s): ? Vertical Asymptotes: ? Horizontal Asymptotes:

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