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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270336

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BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270336
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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