Question

The total cost in dollars to buy uniforms for the players on a volleyball team can be found using the function `c=30.75u+5.75,`where `u` is the number of uniforms bought. If there are at least 8 players but not more than 12 players on the volleyball team, what is the range of the function for this situation?....

Answer 1

To find the range of the function \( c = 30.75u + 5.75 \) given that \( u \) (the number of uniforms) is at least 8 but not more than 12, we will evaluate the function at the endpoints of this interval.

1. Calculate the cost when \( u = 8 \):
\[
c(8) = 30.75(8) + 5.75
\]
\[
c(8) = 246 + 5.75 = 251.75
\]

2. Calculate the cost when \( u = 12 \):
\[
c(12) = 30.75(12) + 5.75
\]
\[
c(12) = 369 + 5.75 = 374.75
\]

Now, we have calculated the cost for both cases:
- When \( u = 8 \), \( c = 251.75 \)
- When \( u = 12 \), \( c = 374.75 \)

Since \( c \) is a linear function that increases as \( u \) increases, the range of the function for \( u \) in the interval \([8, 12]\) is:
\[
[251.75, 374.75]
\]

Therefore, the range of the function for the given situation is:
\[
\boxed{[251.75, 374.75]}
\]