In a piecewise function based on the gas station's pricing deal, the function describes two scenarios: one for purchases under 10 gallons and one for purchases of 10 gallons or more.
The function can be written as:
\[ f(x) = \begin{cases} 2.50 & \text{if } x < 10 \ 2.25 & \text{if } x \geq 10 \end{cases} \]
In this case, \(x\) represents the number of gallons purchased.
When creating the graph of this piecewise function:
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For \(x < 10\), the price is $2.50 per gallon, and this would be represented by a solid line for all values of \(x\) from 0 up to (but not including) 10 gallons.
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At \(x = 10\), the price changes to $2.25 per gallon. However, since the price for \(x < 10\) does not include \(x = 10\) (it is strictly less than), you would use an open circle at the point \( (10, 2.50) \) to indicate that this point is not included in the price for that segment of the function.
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Starting from \(x = 10\), the price is now $2.25 per gallon, which means you would have a solid dot at \( (10, 2.25) \) indicating that the price is $2.25 starting from 10 gallons onward.
Thus, the point that would have an open circle would be \( (10, 2.50) \).