Chapter 4: Q. 30 (page 234)

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

Short Answer

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The graph is

Step by step solution

Given information

Given function $G (x) = \frac{x^{2} - x - 12}{x + 1}$

Factoring the numerator and denominator

Factoring, we get

$G (x) = \frac{x^{2} - x - 12}{x + 1} G (x) = \frac{x^{2} - 4 x + 3 x - 12}{x + 1} G (x) = \frac{x (x - 4) + 3 (x - 4)}{x + 1} G (x) = \frac{(x + 3) (x - 4)}{x + 1}$

Calculate the domain

Setting denominator to zero, we get

$x + 1 = 0 x = - 1$

The domain is all real numbers except $- 1$

Calculate the x intercept

Setting numerator to zero, we get

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

The $y$ intercept is $G (0) = - 12$ i.e. $(0, - 12)$

Calculate the vertical asymptote

The vertical asymptote is zeroes of denominator

$x = - 1$

Calculate the horizontal asymptote

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

$G (x) = x - 2 + \frac{- 10}{x + 1}$

$y = x - 2$

$G (x) = \frac{x^{2} - x - 12}{x + 1} = x - 2 x^{2} - x - 12 = (x - 2) (x + 1) 0 = 10$

This is not true so it doesn't intersect $R$

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.
$G (x) = \frac{x^{2} - x - 12}{x + 1}$

Short Answer

Step by step solution

Given information

Factoring the numerator and denominator

Calculate the domain

Calculate the x intercept

Calculate the vertical asymptote

Calculate the 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 7 on page 228 to analyze the graph of each function.G(x)=x2-x-12x+1

Short Answer

Step by step solution

Given information

Factoring the numerator and denominator

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

Logic and Functions

Statistics

Probability and Statistics

Geometry

Theoretical and Mathematical Physics

Mechanics 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.
$G (x) = \frac{x^{2} - x - 12}{x + 1}$