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: 31b


Technology used: desmos online calculator, $f(x)=\{-4\leq x<0:x,\ \ 0\leq x\leq 0:2\}$ $f(0)=2$ .

Work Step by Step

$f(x)=\left\{\begin{array}{lll} x & if & -4\leq x<0\\ 2 & if & 0\leq x\leq 4 \end{array}\right.$ We build two tables, one for $-4\leq x<0$, 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) another for $0\leq x\leq 4$ we join the endpoints with a line segment, since both 0 and 4 belong to this interval, we draw a solid circles around the endpoints (0,2) and (4,2) $x=0$ belongs to the interval $0\leq x\leq 4$, so we use the rule for that interval $f(0)=2$ For the technology used ( online calc) The technology formula for piecewise defined function has teh form: $f(x)=\text{\{$ interval:expression, interval:expression $\}}$ Here: $f(x)=\{-4\leq x<0:x,\ \ 0\leq x\leq 0:2\}$
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