Chapter 4: Q. 20 (page 234)

In Problems 7-44, follow Steps 1 through 7 on page 228 to analyze the graph of each function.
$G (x) = \frac{3 x}{x^{2} - 1}$

Short Answer

Expert verified

The graph is

Step by step solution

Given information

Given function $G (x) = \frac{3 x}{x^{2} - 1}$

Calculating the domain

Setting the denominator to zero, we get

$x^{2} - 1 = 0 x = \pm 1$

The domain is all real numbers except $1, - 1$

Factoring the numerator and denominator

Factoring, we get

$G (x) = \frac{3 x}{x^{2} - 1} G (x) = \frac{3 x}{(x - 1) (x + 1)}$

Calculate the x intercept

Setting denominator to zero, we get

$3 x = 0 x = 0$

$G (0) = 0$

Calculate the vertical asymptote

Setting to zero, we get

$x^{2} - 1 = 0 x^{2} = 1 x = \pm 1$ is the vertical asymptote

Calculating the horizontal asymptote

Here degree of numerator is less than denominator so the asymptote is $y = 0$

$G (x) = \frac{3 x}{x^{2} - 1} = 0 x = 0$

So the intersection point is $(0, 0)$

Sketching the graph

The graph is

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In Problems 7-44, follow Steps 1 through 7 on page 228 to analyze the graph of each function.
$G (x) = \frac{3 x}{x^{2} - 1}$

Short Answer

Step by step solution

Given information

Calculating the domain

Factoring the numerator and denominator

Calculate the x intercept

Calculate the vertical asymptote

Calculating the horizontal asymptote

Sketching the graph

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In Problems 7-44, follow Steps 1 through 7 on page 228 to analyze the graph of each function.G(x)=3xx2-1

Short Answer

Step by step solution

Given information

Calculating the domain

Factoring the numerator and denominator

Calculate the x intercept

Calculate the vertical asymptote

Calculating the horizontal asymptote

Sketching the graph

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Statistics

Discrete Mathematics

Pure Maths

Mechanics Maths

Logic and Functions

Study anywhere. Anytime. Across all devices.

In Problems 7-44, follow Steps 1 through 7 on page 228 to analyze the graph of each function.
$G (x) = \frac{3 x}{x^{2} - 1}$