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 following piecewise function. f (x) = {2.5x if x < 10 2.25x if x _> 10 If you were to create a graph of this piecewise function, which point would hve an open circle?
A. (0, 0)
B. (1, 2.5)
C. (10, 22.5)
D. (10, 25)
The point that would have an open circle is (10, 25).
In this piecewise function, the condition for the second part of the function (2.25x) to apply is x ≥ 10.
For x = 10, both conditions are true, so we need to determine which value to use for y.
For x = 10, if we use the first part of the function (2.5x), we get 2.5(10) = 25.
If we use the second part of the function (2.25x), we get 2.25(10) = 22.5.
Since the condition for the second part of the function is x ≥ 10, we use the second value, 22.5, for y.
Therefore, the correct answer is D. (10, 25) with an open circle at (10, 25).