Question
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)<
/0>=
⎩
⎨
⎧
2.5x
3.5x
5x
if 0<x<20
if 20≤x≤50
if x>50
What would be the last point graphed on the first piece of the function, f(x)=2.5x?
Answer Box:
(
00
,
00
)
f(x)<
/0>=
⎩
⎨
⎧
2.5x
3.5x
5x
if 0<x<20
if 20≤x≤50
if x>50
What would be the last point graphed on the first piece of the function, f(x)=2.5x?
Answer Box:
(
00
,
00
)
Answers
Answered by
GPT-4o mini
To find the last point graphed on the first piece of the piecewise function \( f(x) = 2.5x \) for \( 0 < x < 20 \), we need to determine the point at the upper boundary of this interval, which is \( x = 20 \).
To find the function value at this point, we substitute \( x = 20 \) into the function:
\[
f(20) = 2.5 \times 20 = 50
\]
Since the piece \( f(x) = 2.5x \) only applies for values of \( x \) up to but not including 20, the last point graphed in this piece is \( (20, 50) \).
However, since the function does not include 20 in this interval, the actual last point we can graph would be just below \( 20 \). A common representation is to state it as the point approaching the boundary:
Thus, we conclude:
\[
\text{Last point on the graph for } f(x) = 2.5x: \quad (20, 50)
\]
So, the answer in the requested format would be:
(20, 50)
To find the function value at this point, we substitute \( x = 20 \) into the function:
\[
f(20) = 2.5 \times 20 = 50
\]
Since the piece \( f(x) = 2.5x \) only applies for values of \( x \) up to but not including 20, the last point graphed in this piece is \( (20, 50) \).
However, since the function does not include 20 in this interval, the actual last point we can graph would be just below \( 20 \). A common representation is to state it as the point approaching the boundary:
Thus, we conclude:
\[
\text{Last point on the graph for } f(x) = 2.5x: \quad (20, 50)
\]
So, the answer in the requested format would be:
(20, 50)