Question

The fee for charging an electric car at Station A is $2 to start and $4 for each hour or fraction of an hour. Which point is NOT included in the graph of this step function?
A. (2.5, 14)
B. (2, 10)
C. (0, 0)
D. (1, 6)

Answer 1

To determine which point is NOT included in the graph of the charging fee function, we first need to calculate the costs based on the function's pricing structure.

The fee to start is $2, and you then have to pay $4 for each hour or fraction of an hour.

1. **For 0 hours (0 – 1 hour):**
- Cost = $2 (only the starting fee)
- Point: (0, 2)

2. **For 1 hour (1 – 2 hours):**
- Cost = $2 + $4 * 1 = $6
- Point: (1, 6)

3. **For 2 hours (2 – 3 hours):**
- Cost = $2 + $4 * 2 = $10
- Point: (2, 10)

4. **For 2.5 hours (2 – 3 hours):**
- Cost = $2 + $4 * 3 (since it's a fraction of an hour) = $14
- Point: (2.5, 14)

Now, let's evaluate the points:

A. (2.5, 14): This is included because 2.5 hours is charged as 3 full hours (total cost = $14).

B. (2, 10): This is included because 2 hours costs $10.

C. (0, 0): This is NOT included because the minimum charge starts at $2.

D. (1, 6): This is included as it corresponds to the cost for 1 hour, which is $6.

Thus, the point that is NOT included in the graph of this step function is:

**C. (0, 0)**.