Chapter 4: Q. 18 (page 234)

In Problems $7 - 44$ , follow Steps 1 through $7$ on page $228$ to analyze the graph of each function.
$R (x) = \frac{x^{2} + x - 12}{x^{2} - 4}$

Short Answer

Expert verified

The graph is

Step by step solution

Given information

Given the function $R (x) = \frac{x^{2} + x - 12}{x^{2} - 4}$

Factor the numerator and denominator

Factoring, we get

$R (x) = \frac{x^{2} + x - 12}{x^{2} - 4} R (x) = \frac{x^{2} + 4 x - 3 x - 12}{(x - 2) (x + 2)} R (x) = \frac{x (x + 4) - 3 (x + 4)}{(x - 2) (x + 2)} R (x) = \frac{(x - 3) (x + 4)}{(x - 2) (x + 2)}$

Calculate the domain

On setting the denominator to zero, we get

$x = - 2, 2$

Substitute numerator equal to zero to get the x intercept

Substituting, we get

$(x - 3) (x + 4) = 0 x = 3, - 4$

The $x$ intercept is $(3, 0), (- 4, 0)$

The $y$ intercept is $R (0) = 3$

Calculate the vertical asymptote

Substituting the denominator to zero, we get

$(x - 2) (x + 2) = 0 x = - 2, 2$ is the vertical asymptote

Calculation of horizontal asymptote

Here the degree of numerator and denominator is same so the horizontal asymptote is

$y = \frac{a}{b} y = \frac{1}{1} y = 1$

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.
$R (x) = \frac{x^{2} + x - 12}{x^{2} - 4}$

Short Answer

Step by step solution

Given information

Factor the numerator and denominator

Calculate the domain

Substitute numerator equal to zero to get the x intercept

Calculate the vertical asymptote

Calculation of horizontal asymptote

Sketching the graph

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Most popular questions from this chapter

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In Problems 7-44, follow Steps 1 through 7on page 228to analyze the graph of each function.R(x)=x2+x-12x2-4

Short Answer

Step by step solution

Given information

Factor the numerator and denominator

Calculate the domain

Substitute numerator equal to zero to get the x intercept

Calculate the vertical asymptote

Calculation of horizontal asymptote

Sketching the graph

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Pure Maths

Logic and Functions

Geometry

Discrete Mathematics

Decision Maths

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.
$R (x) = \frac{x^{2} + x - 12}{x^{2} - 4}$