To analyze the piecewise function given:
\[ f(x) = \begin{cases} 2.5x & \text{if } x < 10 \ 2.25x & \text{if } x \geq 10 \end{cases} \]
We need to determine the behavior of the function around the point \(x = 10\).
-
For \(x < 10\), \(f(x) = 2.5x\). When \(x = 10\), this part does not apply, and the value would be \(2.5(10) = 25\). This means at \(x = 10\) there would be an output of 25 from this equation if it were applicable.
-
For \(x \geq 10\), \(f(x) = 2.25x\). When \(x = 10\): \[ f(10) = 2.25(10) = 22.5 \]
At \(x = 10\), the function transitions from one piece to the other. It would have a value of 25 from the first piece (not included since \(x = 10\) is not less than 10) and a value of 22.5 from the second piece (included). Therefore, there will be an open circle at the point \( (10, 25) \) since that point is not included in the graph of the function.
Thus, the correct answer for the point that would have an open circle is \( (10, 25) \).