Chapter 4: Q. 31 (page 245)

Find the domain of each rational function. Find any horizontal, vertical, or oblique asymptotes.
$R (x) = \frac{x + 2}{x^{2} - 9}$

Short Answer

Expert verified

The domain of the function is $\{x | x \neq - 3, x \neq 3\}$ and vertical asymptotes are $x = 3, x = - 3$ and horizontal asymptote is $y = 0$

Step by step solution

Step 1. Given Information

The given function is $R (x) = \frac{x + 2}{x^{2} - 9}$

Step 2. Explanation

The domain of the function is the set of all real numbers except for all those values for which denominator is 0.

Substitute $x^{2} - 9 = 0$ and solve.

$x^{2} - 9 = 0 (x + 3) (x - 3) = 0 x = - 3, 3$

Step 3. Explanation

The vertical asymptote is the point at which $x^{2} - 9 = 0$

Thus, the vertical asymptotes are $x = - 3, 3$

If a rational function is proper, then $y = 0$ is a horizontal asymptote of the graph of rational function.

Thus, horizontal asymptote is $y = 0$

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Find the domain of each rational function. Find any horizontal, vertical, or oblique asymptotes.
$R (x) = \frac{x + 2}{x^{2} - 9}$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Explanation

Step 3. Explanation

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Find the domain of each rational function. Find any horizontal, vertical, or oblique asymptotes.R(x)=x+2x2-9

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Explanation

Step 3. Explanation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

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Study anywhere. Anytime. Across all devices.

Find the domain of each rational function. Find any horizontal, vertical, or oblique asymptotes.
$R (x) = \frac{x + 2}{x^{2} - 9}$