1. The problem asks us to find the values of $h(x)$ at $x = 3.999$, $4$, $4.0001$, and $9$ based on the graph's description. 2. From the graph description: - For $x$ between $-9$ and $-4$, $h(x) = -9$, with a closed circle at $(-9,-9)$ and open at $(-4,-9)$. - For $x$ between $-7$ and $-3$, $h(x) = 7$, closed at $(-7,7)$ and open at $(-3,7)$. - For $x$ between $5$ and $9$, $h(x) = -2$, open at $(5,-2)$ and closed at $(9,-2)$. 3. Evaluate each: - $h(3.999)$: $3.999$ lies between $-3$ and $5$, but none of the line segments cover this interval. Therefore, $h(3.999)$ is \textbf{Undefined}. - $h(4)$: similarly, $4$ is in the gap between line segments, so $h(4)$ is \textbf{Undefined}. - $h(4.0001)$: same as above, no segment at $4.0001$, so \textbf{Undefined}. - $h(9)$: $9$ is the closed endpoint of the segment where $h(x) = -2$, so $h(9) = -2$. 4. Summary: - $h(3.999) = \text{Undefined}$ - $h(4) = \text{Undefined}$ - $h(4.0001) = \text{Undefined}$ - $h(9) = -2$ Final answers match: $7$ and $-9$ are values on segments that don't include these $x$ values; The only matching value is $-2$ at $h(9)$ and Undefined for the others.