# 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.

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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