Chapter 6: Q. 1 (page 418)

The graph of $y = \frac{3 x - 6}{x - 4}$ has a vertical asymptote. What is it?

Short Answer

Expert verified

The vertical asymptote of the graph is $x = 4$ .

Step by step solution

Step 1. Definition

A rational function $R (x) = \frac{P (x)}{Q (x)}$ , in lowest terms, will have a vertical asymptote $x = r$ if $r$ is a real zero of the denominator $Q (x)$ .

Step 2. Find the vertical asymptote

The function $y = \frac{3 x - 6}{x - 4}$ is in lowest terms. The zero of the denominator is $4$ .

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

So the line $x = 4$ is the vertical asymptote of the given rational function.

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The graph of $y = \frac{3 x - 6}{x - 4}$ has a vertical asymptote. What is it?

Short Answer

Step by step solution

Step 1. Definition

Step 2. Find the vertical asymptote

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The graph of y=3x-6x-4 has a vertical asymptote. What is it?

Short Answer

Step by step solution

Step 1. Definition

Step 2. Find the vertical asymptote

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

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Study anywhere. Anytime. Across all devices.

The graph of $y = \frac{3 x - 6}{x - 4}$ has a vertical asymptote. What is it?