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

Question

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
f
(
x
)
=
{
2.5
x

if

0
≤
x
≤
20
3.5
x

if

2
0

<
x
≤
50

5
x



if

x
>
50


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

(1 point)
(
,
)

Answer 1

To determine the last point graphed on the first piece of the function \( f(x) = 2.5x \), we need to look at the domain of that piece.

The piece \( f(x) = 2.5x \) is valid for \( 0 \leq x \leq 20 \). Therefore, the last point on this piece will occur at the maximum value of \( x \), which is \( x = 20 \).

To find the corresponding \( f(x) \) value at \( x = 20 \): \[ f(20) = 2.5 \times 20 = 50. \]

Thus, the last point graphed on the piece \( f(x) = 2.5x \) is \( (20, 50) \).

So the final answer is: \[ (20, 50) \]