Chapter 4: Q. 32 (page 234)

In Problems 7-44, follow Steps 1 through 7 on page 228 to analyze the graph of each function.
$R (x) = \frac{(x - 1) (x + 2) (x - 3)}{x (x - 4)^{2}}$

Short Answer

Expert verified

The graph is

Step by step solution

Given information

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

Calculate the domain

Setting denominator to zero, we get

$x {(x - 4)}^{2} = 0 x = 0, 4$

The domain is all real numbers except $0, 4$

Calculate the x intercept

Setting numerator to zero, we get

$(x - 1) (x + 2) (x - 3) = 0 x = 1, - 2, 3$

There is no $y$ intercept

Calculate the vertical asymptote

The zeroes of denominator is $x = 0, 4$ so the vertical asymptote is $x = 0, 4$

Calculate the horizontal asymptote

The degree of numerator is same as denominator so the horizontal asymptote is

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

$R (x) = \frac{x^{3} - 2 x^{2} - 5 x + 16}{x^{3} - 8 x^{2} + 16} = 1 x^{3} - 2 x^{2} - 5 x + 16 = x^{3} - 8 x^{2} + 16 6 x^{2} - 5 x = 0 x = \frac{5}{6}$

It intersects at $(\frac{5}{6}, 1)$

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

Short Answer

Step by step solution

Given information

Calculate the domain

Calculate the x intercept

Calculate the vertical asymptote

Calculate 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.R(x)=(x-1)(x+2)(x-3)x(x-4)2

Short Answer

Step by step solution

Given information

Calculate the domain

Calculate the x intercept

Calculate the vertical asymptote

Calculate the horizontal asymptote

Sketching the graph

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Discrete Mathematics

Mechanics Maths

Probability and Statistics

Decision Maths

Calculus

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