Question

Question

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

Answer 1

The first piece of the piecewise function is defined as \( f(x) = 2.5x \) for \( 0 \leq x \leq 20 \). This means that \( f(x) \) is valid and graphed for all \( x \) values from 0 to 20, inclusive.

The last point graphed on this piece of the function would be at the upper bound of the interval, which is when \( x = 20 \). To find the corresponding \( f(x) \) value at this point, we calculate:

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

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