Precalculus (6th Edition) Blitzer

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

Chapter 1 - Section 1.3 - More on Functions and Their Graphs - Exercise Set - Page 197: 54

Answer

a) -19 b) 3 c) 31

Work Step by Step

(a) As $-3<0$ , the first part of the piecewise function will be applicable for $x=-3$. $\begin{align} & f\left( x \right)=6x-1 \\ & f\left( -3 \right)=6\left( -3 \right)-1 \\ & f\left( -3 \right)=-18-1 \\ & f\left( -3 \right)=-19 \end{align}$ Hence, the value of $f\left( -3 \right)$ is $-19$. (b) As $x=0$ , the second part of the piecewise function will be applicable for $x=0$. $\begin{align} & f\left( x \right)=7x+3 \\ & f\left( 0 \right)=7\left( 0 \right)+3 \\ & f\left( 0 \right)=0+3 \\ & f\left( 0 \right)=3 \end{align}$ Hence, the value of $f\left( 0 \right)$ is $3$. (c) As $4\ge 0$ , the second part of the piecewise function will be applicable for $x=4$. $\begin{align} & f\left( x \right)=7x+3 \\ & f\left( 0 \right)=7\left( 4 \right)+3 \\ & f\left( 0 \right)=28+3 \\ & f\left( 0 \right)=31 \end{align}$ Hence, the value of $f\left( 4 \right)$ is $31$.
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