Question
The total cost in dollars to buy uniforms for the players on a volleyball team can be found using the function "c" equals 30.7 5 "u" plus 5.7 5 ,c=30.75u+5.75,where "u"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?
Answers
GPT-4o mini
To find the range of the function \( c = 30.75u + 5.75 \) for the number of uniforms \( u \), given that \( u \) (the number of players needing uniforms) must be between 8 and 12 inclusive, we can evaluate the function at these boundaries.
1. Calculate \( c \) when \( u = 8 \):
\[
c = 30.75(8) + 5.75 = 246 + 5.75 = 251.75
\]
2. Calculate \( c \) when \( u = 12 \):
\[
c = 30.75(12) + 5.75 = 369 + 5.75 = 374.75
\]
Thus, as \( u \) varies from 8 to 12, the cost \( c \) will vary from \( 251.75 \) to \( 374.75 \).
Therefore, the range of the function \( c \) for this situation is:
\[
[251.75, 374.75]
\]
1. Calculate \( c \) when \( u = 8 \):
\[
c = 30.75(8) + 5.75 = 246 + 5.75 = 251.75
\]
2. Calculate \( c \) when \( u = 12 \):
\[
c = 30.75(12) + 5.75 = 369 + 5.75 = 374.75
\]
Thus, as \( u \) varies from 8 to 12, the cost \( c \) will vary from \( 251.75 \) to \( 374.75 \).
Therefore, the range of the function \( c \) for this situation is:
\[
[251.75, 374.75]
\]