Chapter 11: Q8. (page 699)

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

Short Answer

Expert verified

The vertical asymptote: $x = - 2$

The horizontal asymptote: $y = 0$

Step by step solution

Step 1. Define a rational function.

A function of the form $y = \frac{p}{q}$ is called a rational function, where $p$ and $q$ are the polynomials and $q \neq 0$ .

Step 2. Define the asymptotes for the rational function in the form y=ax−b+c.

A rational function in the form $y = \frac{a}{x - b} + c, a \neq 0$ , has a vertical asymptote at the $x$ -value that makes the denominator equal zero, $x = b$ and it has a horizontal asymptote at $y = c$ .

Step 3. Calculate the asymptotes for the function y=32x+4.

Observe the rational function $y = \frac{3}{2 x + 4}$ .

For vertical asymptote,

Denominator $= 0$

$\begin{array}{l} 2 x + 4 = 0 \\ 2 x = - 4 \\ x = \frac{- 4}{2} \\ x = - 2 \end{array}$

So, $x = - 2$ is the vertical asymptote.

For horizontal asymptote,

$y = c$

Since, $c = 0$ .

So, $y = 0$ is the horizontal asymptote.

Therefore,

The vertical asymptote: $x = - 2$

The horizontal asymptote: $y = 0$

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

Short Answer

Step by step solution

Step 1. Define a rational function.

Step 2. Define the asymptotes for the rational function in the form y=ax−b+c.

Step 3. Calculate the asymptotes for the function y=32x+4.

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Identify the asymptotes of the function.y=32x+4

Short Answer

Step by step solution

Step 1. Define a rational function.

Step 2. Define the asymptotes for the rational function in the form y=ax−b+c.

Step 3. Calculate the asymptotes for the function y=32x+4.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Applied Mathematics

Probability and Statistics

Theoretical and Mathematical Physics

Logic and Functions

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

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