Q. 5 - Precalculus Enhanced with Graphing Utilities

Question

Answers are given at the end of these exercises. If you get a wrong answer, read the pages listed in red.

True or False 

The function $f\left(x\right)=\frac{2x}{x-3}$ has $y=2$ as a horizontal asymptote.

Step-by-Step Solution

Answer

True. The function $f\left(x\right)=\frac{2x}{x-3}$ has $y=2$ as a horizontal asymptote.

Step 1. Given

The function $f\left(x\right)=\frac{2x}{x-3}$

To find if $y=2$ is a horizontal asymptote.

Step 2. Horizontal asymptote

If, as $x\to \infty ,-\infty$  the values of $R\left(x\right)$approach some fixed number
$L$, then the line $y=L$ is a horizontal asymptote of the graph of $R$.

Step 3. To find the horizontal asymptote

As $x\to \pm \infty$, $y=2$ is a horizontal
asymptote of the graph.