### Home > APCALC > Chapter 5 > Lesson 5.1.2 > Problem5-20

5-20.

Investigate horizontal asymptotes for quotients of linear functions by examining the results of $\lim\limits _ { x \rightarrow \infty } ( \frac { a x + b } { c x + d } )$ for different values of $a, b, c$, and $d$.

1. In complete sentences, summarize your findings.

A horizontal asymptote can be found by evaluating:

$\lim \limits_{x\rightarrow \infty }\left ( \frac{ax+b}{cx+d} \right )=$

(Compare the highest-powered term in the numerator with the highest-powered term in the denominator.)

2. Write the equation of a function that has a horizontal asymptote of $y = 3$ and a vertical asymptote $x = –5$.

Vertical asymptotes can be found by setting the denominator equal to $0$, AFTER you simplify the fraction. As for horizontal asymptotes, see the hint in part (a).

Use the eTool below to visualize the problem.
Click the link at right for the full version of the eTool: Calc 5-20 HW eTool