   Chapter 2, Problem 15RQ ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.If the line x = 1 is a vertical asymptote of y = f(x), then f is not de tined at 1.

To determine

Whether the statement, “If the line x=1 is a vertical asymptote of y=f(x), then f is not defined at 1 ” is true or false.

Explanation

Definition used: A piecewise defined function is one which is defined not by a single equation, but by two or more. Each equation is valid for some interval.

Reason:

Given that the vertical asymptote x=1. The denominator of the function must be x1.

The function may be f(x)=1x1. Here f(1) is not defined.

But the given statement is false since the below example disproves the given statement.

Consider the piecewise defined function,

Let f(x)={1x1

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