To determine the last point graphed on the first piece of the piecewise function \( f(x) = 2.5x \), we need to know the range of \( x \) values for that piece of the function. Typically, for piecewise functions that charge based on weight, the first piece might apply to a certain weight range, often the lightest weights.
Assuming the first piece of the function corresponds to weights of dogs up to a certain weight (let's say up to 10 pounds for example), the last point of the piece would correspond to the highest weight in that range. For this scenario:
- The function is \( f(x) = 2.5x \).
- The last point in the first piece (assumed to be up to 10 pounds) would be at \( x = 10 \).
Now let's calculate this:
\[ f(10) = 2.5 \times 10 = 25 \]
Thus, the last point graphed on the first piece of the function is \( (10, 25) \).
If the exact range of \( x \) for the first piece is different, you would just substitute that upper limit into the function to find the corresponding \( f(x) \).