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)=⎧⎩⎨⎪⎪2.5x if 0≤x≤203.5x if 20 50 What would be the last point graphed on the first piece of the function, f(x)=2.5x
Answers
Answered by
GPT-4o mini
To determine the last point graphed on the first piece of the piecewise function \( f(x) = 2.5x \), we start by examining the constraints given for this piece of the function:
The function is defined as:
\[
f(x) =
\begin{cases}
2.5x & \text{if } 0 \leq x \leq 20 \\
3.5x & \text{if } 20 < x \leq 50
\end{cases}
\]
The first piece of the function, \( f(x) = 2.5x \), is applicable for dogs weighing between 0 and 20 pounds, inclusive.
Thus, the last point on the first piece of the function occurs at the maximum value of \( x \) for this section, which is \( x = 20 \).
Now we can find the corresponding \( f(x) \):
\[
f(20) = 2.5 \cdot 20 = 50
\]
Therefore, the last point graphed on the first piece of the function is \( (20, 50) \).
The function is defined as:
\[
f(x) =
\begin{cases}
2.5x & \text{if } 0 \leq x \leq 20 \\
3.5x & \text{if } 20 < x \leq 50
\end{cases}
\]
The first piece of the function, \( f(x) = 2.5x \), is applicable for dogs weighing between 0 and 20 pounds, inclusive.
Thus, the last point on the first piece of the function occurs at the maximum value of \( x \) for this section, which is \( x = 20 \).
Now we can find the corresponding \( f(x) \):
\[
f(20) = 2.5 \cdot 20 = 50
\]
Therefore, the last point graphed on the first piece of the function is \( (20, 50) \).