Chapter 4: Q. 44 (page 234)

In Problems 7-44, follow Steps 1 through 7 on page 228 to analyze the graph of each function.
$f (x) = 2 x + \frac{9}{x^{3}}$

Short Answer

Expert verified

The graph is

Step by step solution

Given information

Given the function $f (x) = 2 x + \frac{9}{x^{3}}$

Factoring the numerator and denominator

Factoring, we get

$f (x) = 2 x + \frac{9}{x^{3}} f (x) = \frac{2 x^{4} + 9}{x^{3}}$

Calculate the domain

Calculating, we get

$x^{3} = 0 x = 0$

The domain is all real numbers $0$

Calculate the x intercept

Setting numerator to zero, we get

$2 x^{4} + 9 = 0 x^{4} = - \frac{9}{2}$

There is no $x, y$ intercept

Calculate the vertical asymptote

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

Calculating the horizontal asymptote

The degree of numerator is greater than denominator so there is an oblique asymptote

$y = 2 x$ is the oblique asymptote

$f (x) = \frac{(2 x^{4} + 9)}{x} = 2 x 2 x^{4} + 9 = 2 x^{2} 2 x^{4} - 2 x^{2} = - 9$

It doesn't intersect $f$

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.
$f (x) = 2 x + \frac{9}{x^{3}}$

Short Answer

Step by step solution

Given information

Factoring the numerator and denominator

Calculate the domain

Calculate the x intercept

Calculate the vertical asymptote

Calculating the horizontal asymptote

Sketching the graph

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Most popular questions from this chapter

Recommended explanations on Math Textbooks

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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.f(x)=2x+9x3

Short Answer

Step by step solution

Given information

Factoring the numerator and denominator

Calculate the domain

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

Geometry

Calculus

Mechanics Maths

Discrete Mathematics

Statistics

Theoretical and Mathematical Physics

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.
$f (x) = 2 x + \frac{9}{x^{3}}$