Finite Math and Applied Calculus (6th Edition)

Published by Brooks Cole
ISBN 10: 1133607705
ISBN 13: 978-1-13360-770-0

Chapter 1 - Section 1.1 - Functions from the Numerical, Algebraic, and Graphical Viewpoints - Exercises - Page 53: 32a

Answer

Technology used: desmos online calculator, $f(x)=\{-4 \leq x \leq 0:-1,\ \ 0 < x \leq 4:x\}$ $f(-1)=-1$ .
1511291822

Work Step by Step

$f(x)=\left\{\begin{array}{lll} -1 & if & -4 \leq x \leq 0\\ x & if & 0 < x \leq 4 \end{array}\right.$ We build two tables, one for $-4\leq x \leq 0$, we join the endpoints with a line segment, since 0 belongs to this interval, we draw a solid circle for the point $(0,-1)$ $-4$ is in the interval, solid circle for the point $(-4,-1)$ another for $0 < x \leq 4$ we join the endpoints with a line segment, since 0 does not belong to this interval, we draw an empty circle for the point $(0,0)$ $4$ is in the interval, solid circle for the point $(4,4)$ $x=-1$ belongs to the interval $-4 \leq x \leq 0$, so we use the rule for that interval $f(-1)=-1$ The technology formula for piecewise defined function has the form: $f(x)=\text{\{$ interval:expression, interval:expression $\}}$ Here: $f(x)=\{-4 \leq x \leq 0:-1,\ \ 0 < x \leq 4:x\}$
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