Chapter 4: Q. 26 (page 234)

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

Short Answer

Expert verified

The graph is

Step by step solution

Given information

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

Factoring the numerator and denominator

Factoring, we get

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

Calculating the domain

Setting denominator to zero, we get

$x - 1 = 0 x = 1$

The domain is all real numbers except $1$

Calculating x intercept

Setting numerator to zero, we get

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

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

Calculating the vertical asymptote

Setting to zero, we get

$x - 1 = 0 x = 1$

Calculating the horizontal asymptote

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

$F (x) = x + 4 + \frac{6}{x - 1}$

The oblique asymptote is $y = x + 4$ and doesn't intersects $F$

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

Short Answer

Step by step solution

Given information

Factoring the numerator and denominator

Calculating the domain

Calculating x intercept

Calculating the vertical asymptote

Calculating 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.F(x)=x2+3x+2x-1

Short Answer

Step by step solution

Given information

Factoring the numerator and denominator

Calculating the domain

Calculating x intercept

Calculating 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

Theoretical and Mathematical Physics

Pure Maths

Probability and Statistics

Decision Maths

Statistics

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