Calculus: Early Transcendentals 9th Edition

Published by Cengage Learning
ISBN 10: 1337613924
ISBN 13: 978-1-33761-392-7

Chapter 1 - Section 1.1 - Four Ways to Represent a Function - 1.1 Exercises - Page 17: 3

Answer

a) $g(-2)=2$, $g(0)=-2$, $g(2)=1$, $g(3)=2.5$ (b) $x=-4$ (c) $\{x|-4\leq x\leq 4\}$. (d) Domain: $\{x|-4\leq x\leq 4\}$ Range: $\{y|-2\leq y\leq 3\}$ (e) $\{x|0\leq x\leq 2\}$.

Work Step by Step

(a) When $x=-2$, we can see that $y=2$. Therefore, $g(-2)=2$ When $x=0$, we can see that $y=-2$. Therefore, $g(0)=-2$ When $x=2$, we can see that $y=1$ because that circle is filled in. The circle at point $(2, 3)$ means the function value is not 3 when $x=2$. Therefore, $g(2)=1$ When $x=3$, we can see that $y=2.5$. Therefore, $g(3)=2.5$ (b) Only when $x=-4$ because as we noted above, $g(x)$ is not 3 when $x=2$. (c) We can see that in the region where g is defined, its value is always less than or equal to 3. Therefore, across the whole domain. $\{x|-4\leq x\leq 4\}$. (d) We see how the function g is defined in the interval when x goes from $-4$ to $4$. Therefore, the domain is $\{x|-4\leq x\leq 4\}$. The y values go from $-2$ to $3$. Therefore, the range is $\{y|-2\leq y\leq 3\}$. (e) The value of g is increasing in the interval $\{x|0\leq x\leq 2\}$.
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