Pearson Algebra 2 Common Core, 2011
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Pearson Algebra 2 Common Core, 2011 View details
Mid-Chapter Quiz
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Exercise 13 Page 526

We want find any holes, as well as the vertical and horizontal asymptotes, in the graph of the function.

Holes and Vertical Asymptotes

Let's start by factoring the denominator.
Recall that division by zero is not defined. Therefore, the rational function is undefined where We will use the Zero Product Property to solve this equation.
The function is not defined when and This means we have either a hole or a vertical asymptote. We cannot simplify the function. This indicates the lines and are vertical asymptotes.

Horizontal Asymptotes

Let's recall how to find horizontal asymptotes in rational functions.

The degree of is greater than the degree of There are no horizontal asymptotes
The degree of is greater than the degree of is a horizontal asymptote
The degrees of and are equal is a horizontal asymptote, where and are the leading coefficients of and respectively
Let's now consider the given function.
Since the degree of the denominator is greater than the degree of the numerator, the line is a horizontal asymptote.