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.

Question

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 point)
Responses

(20, 50)
(20, 50)

(2.5, 5)
(2.5, 5)

(5, 50)

Answer 1

The first piece of the function, \( f(x) = 2.5x \), is defined for the interval \( 0 \leq x \leq 20 \). To find the last point graphed on this segment, we need to evaluate the function at the upper limit of this interval, which is \( x = 20 \).

Calculating \( f(20) \):

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

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

The correct response is:

(20, 50)