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?
a. 0<u\le12
b. 0<c\le374.75
c. \left\{8,\ 9,\ 10,\ 11,\ 12\right\}
d. \left\{251.75,\ 282.50,\ 313.25,\ 344,\ 374.75\right\}

Answer 1

To find the range of the cost function \( c = 30.75u + 5.75 \) for the given number of uniforms \( u \) (which ranges from 8 to 12), we can calculate the cost at the minimum and maximum values of \( u \).

First, we calculate the cost when \( u = 8 \):

\[
c = 30.75(8) + 5.75
\]
\[
c = 246 + 5.75
\]
\[
c = 251.75
\]

Next, we calculate the cost when \( u = 12 \):

\[
c = 30.75(12) + 5.75
\]
\[
c = 369 + 5.75
\]
\[
c = 374.75
\]

Now, we find the range of \( c \) when \( u \) varies from 8 to 12. The minimum cost occurs at \( u = 8 \) and is \( c = 251.75 \), while the maximum cost occurs at \( u = 12 \) and is \( c = 374.75 \).

Thus, the range of the function for the situation specified (number of uniforms from 8 to 12) is:

\[
\{ 251.75, 282.50, 313.25, 344.00, 374.75 \}
\]

So the correct answer is:

d. \(\left\{251.75,\ 282.50,\ 313.25,\ 344,\ 374.75\right\}\)