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Consider the function h(x) = \frac{x^2-9}{x^2-4} . a. Find the domain of h(x) . b. Find the...

Question:

Consider the function {eq}h(x) = \frac{x^2-9}{x^2-4} {/eq}.

a. Find the domain of {eq}h(x) {/eq}.

b. Find the x- and y- intercepts.

c. Is {eq}h(x) {/eq} even or odd ?

d. Find the horizontal and vertical asymptotes.

Analyzing Rational Functions

A rational function is a function of the form: {eq}f(x)=\frac{g(x)}{h(x)} {/eq}. This function has vertical asymptotes at those values of {eq}x {/eq} that satisfy {eq}h(x)=0 {/eq} when the function is in reduced form. This function has a horizontal asymptote when the degree {eq}h(x) {/eq} is greater than or equal to the degree of {eq}g(x) {/eq}.

Answer and Explanation:

a. The domain of this function will be all values of {eq}x {/eq} except those make the denominator equal to 0.

{eq}x^2-4=0\\ (x-2)(x+2)=0...

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Analyzing the Graph of a Rational Function: Asymptotes, Domain, and Range

from Math 105: Precalculus Algebra

Chapter 4 / Lesson 9
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