1. **State the problem:** We have a piecewise function for a car-sharing service membership fee: $$F(x) = \begin{cases} 50 & \text{if } 0 \leq x \leq 10 \\ 50 + 14(x - 10) & \text{if } x > 10 \end{cases}$$ where $x$ is the number of hours driven in a month. 2. **Find the left-hand limit as $x$ approaches 10:** Since for $x \leq 10$, $F(x) = 50$, the left-hand limit is: $$\lim_{x \to 10^-} F(x) = 50$$ 3. **Find the right-hand limit as $x$ approaches 10:** For $x > 10$, $F(x) = 50 + 14(x - 10)$. Substitute $x = 10$: $$\lim_{x \to 10^+} F(x) = 50 + 14(10 - 10) = 50 + 14 \times 0 = 50$$ 4. **Find the overall limit as $x$ approaches 10:** Since both one-sided limits are equal, $$\lim_{x \to 10} F(x) = 50$$ 5. **Explain the function behavior:** - For $0 \leq x \leq 10$, the fee is a flat $50$. - For $x > 10$, the fee increases by $14$ for each additional hour beyond 10. 6. **Graph description:** - A horizontal line at $y=50$ from $x=0$ to $x=10$. - A line starting at $(10,50)$ with slope $14$ for $x > 10$. This confirms the function is continuous at $x=10$ with the limit equal to 50.