Chapter 4: Q. 25 (page 234)

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

Short Answer

Expert verified

The graph is

Step by step solution

Given information

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

Factoring the numerator and denominator

Factoring, we get

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

Calculating the domain

Setting denominator to zero, we get

$x + 2 = 0 x = - 2$

The domain is all real numbers except $- 2$

Calculating the x intercept

Setting numerator to zero, we get

$(x + 1) (x - 4) = 0 x = - 1, 4$

The $y$ intercept is $F (0) = - 2$ i.e. $(0, - 2)$

Calculating the vertical asymptote

Setting denominator to zero, we get

$x = - 2$

Calculate the horizontal asymptote

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

The oblique asymptote is $y = x - 5$

Sketching the graph

The graph is

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

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

Short Answer

Step by step solution

Given information

Factoring the numerator and denominator

Calculating the domain

Calculating the x intercept

Calculating 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

Pure Maths

Mechanics Maths

Geometry

Discrete Mathematics

Calculus

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.F(x)=x2-3x-4x+2

Short Answer

Step by step solution

Given information

Factoring the numerator and denominator

Calculating the domain

Calculating the x intercept

Calculating 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

Pure Maths

Mechanics Maths

Geometry

Discrete Mathematics

Calculus

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