Chapter 5: Q. 5 (page 282)

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

Short Answer

Expert verified

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

Step by step solution

Step 1. Given

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

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

Step 2. Horizontal asymptote

If, as $x \to \infty, - \infty$ the values of $R (x)$ 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.

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

Short Answer

Step by step solution

Step 1. Given

Step 2. Horizontal asymptote

Step 3. To find the horizontal asymptote

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Answers are given at the end of these exercises. If you get a wrong answer, read the pages listed in red.True or FalseThe function f(x)=2xx-3 hasy=2 as a horizontal asymptote.

Short Answer

Step by step solution

Step 1. Given

Step 2. Horizontal asymptote

Step 3. To find the horizontal asymptote

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Calculus

Decision Maths

Applied Mathematics

Mechanics Maths

Logic and Functions

Study anywhere. Anytime. Across all devices.

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