A dog groomer charges her clients by the weight of the dog. The following piecewise function represents the total charge, f(x)

, for a dog weighing x pounds.

f(x)=⎧⎩⎨⎪⎪2.5x if 0≤x≤203.5x if 20 <x≤50 5x if x>50


What would be the last point graphed on the first piece of the function, f(x)=2.5x
?

1 answer

To find the last point graphed on the first piece of the function \( f(x) = 2.5x \), we need to look at the domain of this piece of the piecewise function, which is defined for \( 0 \leq x \leq 20 \).

The last point of the first piece occurs at the upper limit of this interval, when \( x = 20 \). To find the corresponding value of \( f(20) \):

\[ f(20) = 2.5 \times 20 = 50. \]

Thus, the last point graphed on the first piece of the function is \( (20, 50) \).