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Consider the function below. f (x) = \frac{x^2}{x^2 - 16} (a) Find the vertical and horizontal...

Question:

Consider the function below.

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

(a) Find the vertical and horizontal asymptotes.

(b) Find the interval where the function is Increasing.

Find the interval where the function is decreasing.

(c) Find the local maximum value.

(d) Find the interval where the function is concave up.

Find the interval where the function is concave down.

Rational Functions

Due to having a denominator polynomial, a rational expression may not be defined for all real numbers.

At those numbers, where the denominator is zero, the function may have a vertical asymptote.

Horizontal or any other line asymptotes can only occur for {eq}x \to \pm \infty. {/eq}

Not every rational expression has a horizontal asymptote though.

Answer and Explanation:

a)

Let us observe that we have {eq}f(x)=f(-x), {/eq} that is, the function is reflection symmetric about

the {eq}y {/eq}-axis. We have to check...

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Rational Function: Definition, Equation & Examples

from GMAT Prep: Help and Review

Chapter 10 / Lesson 11
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