Problem

Suppose that the function $h$ is defined on the interval $(-2,2]$ as follows.
\[
h(x)=\left\{\begin{array}{ll}
-1 & \text { if }-2< x \leq-1 \\
0 & \text { if }-1< x \leq 0 \\
1 & \text { if } 0< x \leq 1 \\
2 & \text { if } 1< x \leq 2
\end{array}\right.
\]
Find $h(-1), h(0.5)$, and $h(2)$

Answer

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Answer

\(\boxed{h(-1) = -1, h(0.5) = 1, h(2) = 2}\)

Steps

Step 1 :The function h(x) is defined piecewise, meaning it has different definitions for different intervals of x.

Step 2 :To find h(-1), h(0.5), and h(2), we need to determine which interval each of these values falls into, and then apply the corresponding definition.

Step 3 :For h(-1), -1 falls into the interval -2

Step 4 :For h(0.5), 0.5 falls into the interval 0

Step 5 :For h(2), 2 falls into the interval 1

Step 6 :\(\boxed{h(-1) = -1, h(0.5) = 1, h(2) = 2}\)

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