Chapter 4: Q. 22 (page 234)

In Problems $7 - 44$ , follow Steps 1 through 7 on page 228 to analyze the graph of each function.
$R (x) = \frac{- 4}{(x + 1) (x^{2} - 9)}$

Short Answer

Expert verified

The graph is

Step by step solution

Given information

Given function $R (x) = \frac{- 4}{(x + 1) (x^{2} - 9)}$

Factoring the numerator and denonimator

Factoring, we get

$R (x) = \frac{- 4}{(x + 1) (x^{2} - 9)} R (x) = \frac{- 4}{(x + 1) (x - 3) (x + 3)}$

Calculate the domain

Setting denominator to zero, we get

$(x + 1) (x^{2} - 9) = 0 (x + 1) (x - 3) (x + 3) = 0 x = - 1, 3, - 3$

The domain is all real numbers except $- 1, 3, - 3$

calculate the x intercept

There is no term of $x$ so there is no $x$ intercept

The $y$ is $R (0) = \frac{4}{9}$

Calculate the vertical asymptote

Setting denominator to zero, we get

$x = - 1, 3, - 3$

Calculating horizontal asymptote

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

The intersection point is

$R (x) = \frac{- 4}{x^{3} + x^{2} - 9 x - 9} = 0 - 4 = 0$

It is not true so it doesn't intersects $R$

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.
$R (x) = \frac{- 4}{(x + 1) (x^{2} - 9)}$

Short Answer

Step by step solution

Given information

Factoring the numerator and denonimator

Calculate the domain

calculate the x intercept

Calculate the vertical asymptote

Calculating horizontal asymptote

Sketching the graph

One App. One Place for Learning.

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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)=-4(x+1)x2-9

Short Answer

Step by step solution

Given information

Factoring the numerator and denonimator

Calculate the domain

calculate the x intercept

Calculate the vertical asymptote

Calculating horizontal asymptote

Sketching the graph

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Logic and Functions

Pure Maths

Probability and Statistics

Geometry

Statistics

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.
$R (x) = \frac{- 4}{(x + 1) (x^{2} - 9)}$