1. The problem asks us to write a function notation statement based on the given temperature graph $h(t)$, where $t$ is the number of hours since midnight. 2. From the graph description, the temperature starts near 1 degree at $t=0$, dips below 0 to about -6 degrees between $t=4$ and $t=6$, stays low until about $t=9$, then rises sharply to about 7 degrees at $t=12$. 3. We can express this behavior with a piecewise function $h(t)$ that models the temperature at different times $t$: $$ h(t) = \begin{cases} 1 - 0.5t & \text{for } 0 \leq t < 4 \\ -6 & \text{for } 4 \leq t \leq 9 \\ -6 + 1.857(t - 9) & \text{for } 9 < t \leq 12 \end{cases} $$ 4. Explanation: - From $0$ to $4$ hours, temperature decreases roughly linearly from 1 to about -1 (approximation). - From $4$ to $9$ hours, temperature stays constant near -6 degrees. - From $9$ to $12$ hours, temperature rises sharply from -6 to about 7 degrees. 5. This function notation tells us how temperature changes over time: it decreases early morning, stays cold mid-morning, then warms up sharply by noon. Final answer: $$h(t) = \begin{cases} 1 - 0.5t & 0 \leq t < 4 \\ -6 & 4 \leq t \leq 9 \\ -6 + 1.857(t - 9) & 9 < t \leq 12 \end{cases}$$