/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 128 Determine whether each statement... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 128

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The graph of a rational function can have three vertical asymptotes.

Short Answer

Expert verified
The statement 'The graph of a rational function can have three vertical asymptotes' is true.

Step by step solution

01

Understanding the properties of a rational function

A rational function is any function that can be described as the ratio of two polynomial functions. The vertical asymptotes of a rational function are the x-values that make the denominator of the function equals zero (assuming the numerator is not zero at these points).
02

Analyzing the given statement

The given statement is 'The graph of a rational function can have three vertical asymptotes.' To determine whether this statement is true or false, it is critical to examine the possibility for a rational function to have three distinct x-values which cause the denominator to be zero.
03

Verifying the statement

A rational function can indeed have three vertical asymptotes. For example, consider the function \( f(x) = \frac{1}{(x-a)(x-b)(x-c)} \), where a, b, and c are distinct real numbers. In this case, a, b, and c will be the vertical asymptotes because the function will approach infinity at these points. Therefore, we conclude that the given statement is true.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Solve each inequality in Exercises \(65-70\) and graph the solution set on a real number line. $$ \frac{x^{2}-x-2}{x^{2}-4 x+3}>0 $$

What is a polynomial incquality?

Exercises will help you prepare for the material covered in the next section. If \(f(x)=x^{3}-2 x-5,\) find \(f(2)\) and \(f(3) .\) Then explain why the continuous graph of \(f\) must cross the \(x\) -axis between 2 and 3.

Use long division to rewrite the equation for \(g\) in the form $$\text {quotient }+\frac{\text {remainder}}{\text {divisor}}$$ Then use this form of the function's equation and transformations. $$g(x)=\frac{3 x-7}{x-2}$$

Determine whether each statement makes sense or does not make sense, and explain your reasoning. As production level increases, the average cost for a company to produce each unit of its product also increases.
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Geometry

Read Explanation

Mechanics Maths

Read Explanation

Decision Maths

Read Explanation

Logic and Functions

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.