Consider the following. \\ g(x) = \frac{x^2 - x -6}{x^2 - 16}\\ (a) State the domain of the...

Question:

Consider the following.

{eq}g(x) = \frac{x^2 - x -6}{x^2 - 16}{/eq}

(a) State the domain of the function.

(b) Identify all intercepts.

(c) Find any vertical and horizontal asymptotes.

Rational Functions

A rational function is a function with the form {eq}f(x) = \frac{P(x)}{Q(x)} {/eq} where {eq}P(x) {/eq} and {eq}Q(x) {/eq} are polynomials, and {eq}Q(x) \neq 0 {/eq}. The domain of a rational function is the set of all possible real number values of {eq}x {/eq} except the {eq}x {/eq}-values that would make the denominator equal to zero. Lastly, an asymptote is a line that approaches the graph of a rational function but never actually meets it. There are two types asymptote: vertical and horizontal asymptote, and the ways to solve them are different.

Answer and Explanation:

a) To identify the domain of the given function, we must solve the roots of the denominator to know the restricted values of {eq}x {/eq}:

{eq}\begin...

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Expressions of Rational Functions

from Precalculus: High School

Chapter 13 / Lesson 4
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