Question

A gas station is offering a deal. If you buy 10 gallons or more of gas, you will be charged $2.25 per gallon instead of the regular $2.50 per gallon. The deal is modeled by the following piecewise function.

f(x)={2.5x if x<102.25x if x≥10

If you were to create a graph of this piecewise function, which point would have an open circle?

(1 point)
Responses

(1,2.5)
left parenthesis 1 comma 2.5 right parenthesis

(10,22.5)
left parenthesis 10 comma 22.5 right parenthesis

(0,0)
left parenthesis 0 comma 0 right parenthesis

(10,25)
left parenthesis 10 comma 25 right parenthesis
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Answer 1

To determine where the open circle would be located in the piecewise function given, we need to evaluate the transition point at \( x = 10 \).

The function is defined as follows:

- For \( x < 10 \): \( f(x) = 2.5x \)
- For \( x \geq 10 \): \( f(x) = 2.25x \)

At \( x = 10 \):
- When using the first part of the function (for \( x < 10 \)), we calculate \( f(10) = 2.5 \times 10 = 25 \).
- When using the second part of the function (for \( x \geq 10 \)), we calculate \( f(10) = 2.25 \times 10 = 22.5 \).

Since the function changes at \( x = 10 \), it means that the point \( (10, 25) \) from the first part does not actually belong to the function (as it is defined for \( x < 10 \)), and thus it will have an open circle.

Therefore, the point that has an open circle is:

\((10, 25)\).