Chapter 4: Q. 7 (page 234)

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

Short Answer

Expert verified

The graph for the function $R (x) = \frac{x + 1}{x (x + 4)}$ is,

Step by step solution

Step 1 Given function is,

$R (x) = \frac{x + 1}{x (x + 4)}$

The domain of $R$ is, $\{x | x \neq 0, - 4\}$ .

As the value $0$ does not in the domain, there is no $y$ -intercept.

The function $R$ is in the lowest terms.

The real zero of the numerator satisfies the equation $x + 1 = 0$ . So, the $x$ - intercept is, $- 1$ .

Step 2 The real zeros of the denominator are the real solutions of the equation.

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

The lines $x = 0, x = - 4$ are the vertical asymptotes of the graph.

In the given function, the degree of the numerator is less than the degree of the denominator. So, $R$ is proper.

So, the line $y = 0$ is the horizontal asymptote of the graph.

Substitute $R (x) = 0$ in the given equation.

$\frac{x + 1}{x (x + 4)} = 0 x + 1 = 0 x = - 1$

So, the graph intersects the horizontal asymptote at $(- 1, 0)$ .

Step 3 Now plot a graph by using the known values.

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

Short Answer

Step by step solution

Step 1 Given function is,

Step 2 The real zeros of the denominator are the real solutions of the equation.

Step 3 Now plot a graph by using the known values.

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In Problems 7-44, follow Steps 1through 7on page 228to analyze the graph of each function.Rx=x+1xx+4

Short Answer

Step by step solution

Step 1 Given function is,

Step 2 The real zeros of the denominator are the real solutions of the equation.

Step 3 Now plot a graph by using the known values.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Mechanics Maths

Statistics

Probability and Statistics

Geometry

Discrete Mathematics

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.
$R (x) = \frac{x + 1}{x (x + 4)}$