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?
(2.5,14), (2,10), (0,0) or (1,6)
(2.5,14), (2,10), (0,0) or (1,6)
Answers
GPT-4o mini
To determine which point is NOT included in the graph of the charging fee function, let's analyze the fee structure.
1. The starting fee is $2.
2. After the first hour, it costs $4 for each hour or fraction of an hour.
We can break down the total cost based on the time spent charging:
- For 0 hours: Cost is $2 (this corresponds to the point (0, 0) as there is no charge before the start).
- For any time up to 1 hour (0 < time ≤ 1): Cost is $2 + $4 * 1 = $6 (this means $6 for any time in this range).
- So, (0.5, 6) is included, but since 1 hour's fraction will also count as $6 until the next hour.
- For 1 hour to 2 hours (1 < time ≤ 2): Cost is $2 + $4 * 2 = $10 (this corresponds to points like (1.5, 10)).
- For 2 hours to 3 hours (2 < time ≤ 3): Cost is $2 + $4 * 3 = $14 (this corresponds to points like (2.5, 14)).
Now let's evaluate each point given:
- (0, 0): This is the starting point before any charges are applied, which is valid according to the fee structure.
- (1, 6): This is valid, as charging for any time from 0 to just under 1 hour is charged as $6.
- (2, 10): This point is valid, as charging for 2 hours results in a cost of $10 due to the flat fee and the hourly charge.
- (2.5, 14): This point is valid since charging for 2.5 hours results in a cost of $14.
However, the point (1, 6) actually should only be obtained when the charge is specifically at 1 hour, which will be $6, but if time for charging is between (1, 2], then all charges are at the same price.
Thus, (1, 6) should be excluded from being valid since it is directly calculated on the edges of the time.
So, the answer is that the point **(1, 6)** is NOT included in the graph of this step function.
1. The starting fee is $2.
2. After the first hour, it costs $4 for each hour or fraction of an hour.
We can break down the total cost based on the time spent charging:
- For 0 hours: Cost is $2 (this corresponds to the point (0, 0) as there is no charge before the start).
- For any time up to 1 hour (0 < time ≤ 1): Cost is $2 + $4 * 1 = $6 (this means $6 for any time in this range).
- So, (0.5, 6) is included, but since 1 hour's fraction will also count as $6 until the next hour.
- For 1 hour to 2 hours (1 < time ≤ 2): Cost is $2 + $4 * 2 = $10 (this corresponds to points like (1.5, 10)).
- For 2 hours to 3 hours (2 < time ≤ 3): Cost is $2 + $4 * 3 = $14 (this corresponds to points like (2.5, 14)).
Now let's evaluate each point given:
- (0, 0): This is the starting point before any charges are applied, which is valid according to the fee structure.
- (1, 6): This is valid, as charging for any time from 0 to just under 1 hour is charged as $6.
- (2, 10): This point is valid, as charging for 2 hours results in a cost of $10 due to the flat fee and the hourly charge.
- (2.5, 14): This point is valid since charging for 2.5 hours results in a cost of $14.
However, the point (1, 6) actually should only be obtained when the charge is specifically at 1 hour, which will be $6, but if time for charging is between (1, 2], then all charges are at the same price.
Thus, (1, 6) should be excluded from being valid since it is directly calculated on the edges of the time.
So, the answer is that the point **(1, 6)** is NOT included in the graph of this step function.