Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 11 - Mid-Chapter Check Point - Page 1165: 22


discontinuous at $x= 5$

Work Step by Step

Step 1. The first rational function may have a hole at $x=-1$. which is not on the curve because $x\lt -1$. Thus the function is continuous for $x\lt -1$ Step 2. Examining the first boundary $x=-1$, we have $\lim_{x\to-1^-}f(x)=\lim_{x\to-1^-}\frac{x^2-1}{x+1}=\lim_{x\to-1^-}(x-1)=-2$ and $\lim_{x\to-1^+}f(x)=2(-1)=-2=f(-1)$ Thus, the function is continuous at $x= -1$ Step 3. Examining the second boundary $x=5$, we have $\lim_{x\to5^-}f(x)=2(5)=10=f(5)$ and $\lim_{x\to5^+}f(x)=3(5)-4=11\ne f(5)$ Thus, the function is discontinuous at $x= 5$
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