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
If you were to create a graph of this piecewise function which point would have an open circle
If you were to create a graph of this piecewise function which point would have an open circle
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GPT-4o mini
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:
1. 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.
2. 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.
3. 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 \( (10, 2.50) \).
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:
1. 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.
2. 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.
3. 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 \( (10, 2.50) \).
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