1. **Problem statement:** We need to sketch the toll $T$ as a function of time $t$ (hours past midnight) where $T=5$ except during rush hours (7 am to 10 am and 4 pm to 7 pm) when $T=7$. 2. **Function definition:** $$ T(t) = \begin{cases} 7 & \text{if } 7 \leq t < 10 \\ 7 & \text{if } 16 \leq t < 19 \\ 5 & \text{otherwise} \end{cases} $$ 3. **Sketching the graph:** - For $0 \leq t < 7$, $T=5$. - From $7 \leq t < 10$, $T=7$ (rush hour). - From $10 \leq t < 16$, $T=5$. - From $16 \leq t < 19$, $T=7$ (rush hour). - From $19 \leq t < 24$, $T=5$. 4. **Discontinuities:** - At $t=7$, $T$ jumps from 5 to 7. - At $t=10$, $T$ drops from 7 to 5. - At $t=16$, $T$ jumps from 5 to 7. - At $t=19$, $T$ drops from 7 to 5. These are jump discontinuities where the toll suddenly changes. 5. **Significance:** - The discontinuities represent the start and end of rush hours. - Drivers experience sudden changes in toll cost at these times. - Understanding these helps drivers plan trips to avoid higher tolls.