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 find which point on the graph where the function changes from one rule to the other would be represented by an open circle.
The function changes at \( x = 10 \). For \( x \) values less than 10, the function follows the first rule, \( f(x) = 2.5x \). At \( x = 10 \):
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When we evaluate from the first piece, \( f(10) \) using \( 2.5x \): \[ f(10) = 2.5 \times 10 = 25 \]
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When we evaluate from the second piece, \( f(10) \) using \( 2.25x \): \[ f(10) = 2.25 \times 10 = 22.5 \]
The value at \( x = 10 \) is \( 25 \) from the first piece (for \( x < 10 \)) and \( 22.5 \) from the second piece (for \( x \geq 10 \)). Therefore, the function does not include the point \( (10, 25) \) since it only applies for \( x < 10 \).
Thus, the graph will have an open circle at the point \( (10, 25) \) because the function value does not actually reach that point; it approaches it from the left side.
The correct answer is: (10, 25)