Chapter 11: Q9. (page 699)

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

Short Answer

Expert verified

The vertical asymptote: $x = 4$

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=2x−4.

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

For vertical asymptote,

Denominator $= 0$

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

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: $x = 4$

The horizontal asymptote: $y = 0$

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

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=2x−4.

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Identify the asymptotes of the function.y=2x−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=2x−4.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

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Pure Maths

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Decision Maths

Study anywhere. Anytime. Across all devices.

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