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.

Question

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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GPT-4o mini · Answer

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:

$(10, 25)$.