Chapter 11: Q26. (page 731)

Identify the asymptotes of each function.
$y = \frac{4}{x^{2} + 3 x - 28} + 2$

Short Answer

Expert verified

The asymptotes of the given function are $x = 4$ , $x = - 7$ and $y = 2$ .

Step by step solution

Step 1. Define asymptotes.

A rational function which is in the form of $y = \frac{a}{x - b} + c$ , $a \neq 0$ has a horizontal asymptote at $y = c$ and a vertical asymptote at $x = b$ .

Step 2. Set a denominator equal to zero.

Set a denominator of a given expression equal to zero.

$x^{2} + 3 x - 28 = 0$

Step 3. Factor and simplify.

Factor the above equation and simplify further.

$(x - 4) (x + 7) = 0 (x - 4) = 0 or (x + 7) = 0 x = 4 x = - 7$

Therefore, the vertical asymptotes are $x = 4$ and $x = - 7$ . Horizontal asymptote is $y = 2$ .

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Identify the asymptotes of each function.
$y = \frac{4}{x^{2} + 3 x - 28} + 2$

Short Answer

Step by step solution

Step 1. Define asymptotes.

Step 2. Set a denominator equal to zero.

Step 3. Factor and simplify.

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Identify the asymptotes of each function.y=4x2+3x−28+2

Short Answer

Step by step solution

Step 1. Define asymptotes.

Step 2. Set a denominator equal to zero.

Step 3. Factor and simplify.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Mechanics Maths

Applied Mathematics

Geometry

Calculus

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Identify the asymptotes of each function.
$y = \frac{4}{x^{2} + 3 x - 28} + 2$