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 $\{x|0\leq x\leq 2\}$.
