A coach is buying new soccer balls for the team. The total cost can be found using this function c(b)=6.25b+5.50. The coach needs to buy at least 6 balls but no more than 15.
What is the range of this function?
The range of a function is the set of all possible output values. In this case, the cost is the output value, which is determined by the number of balls purchased (the input value).
To find the range, we need to consider the minimum and maximum number of balls the coach can buy. The minimum is 6 balls and the maximum is 15 balls.
Substituting these values into the function, we get:
c(6) = 6.25(6) + 5.50 = 37.50 + 5.50 = 43.00
c(15) = 6.25(15) + 5.50 = 93.75 + 5.50 = 99.25
So the function outputs a minimum cost of $43.00 and a maximum cost of $99.25.
Therefore, the range of this function is the set of all possible costs, which is $43.00 to $99.25.
that is incorrect
Apologies for the mistake.
To correct it, let's consider the minimum and maximum numbers of balls the coach can buy, which are 6 and 15, respectively.
Substituting these values into the function, we get:
c(6) = 6.25(6) + 5.50 = 37.50 + 5.50 = 43.00
c(15) = 6.25(15) + 5.50 = 93.75 + 5.50 = 99.25
Therefore, the range of this function is the set of all possible costs, which is $43.00 to $99.25.
To find the range of the function c(b) = 6.25b + 5.50, we need to determine the possible values that the function can output.
In this case, the function represents the total cost (c) of buying soccer balls, given the number of balls (b). The function involves multiplying the number of balls by 6.25 and adding 5.50.
Since the number of balls (b) must be at least 6 and no more than 15, we can substitute these values into the function to find the range:
For b = 6:
c(6) = 6.25(6) + 5.50
c(6) = 37.50 + 5.50
c(6) = 43.00
For b = 15:
c(15) = 6.25(15) + 5.50
c(15) = 93.75 + 5.50
c(15) = 99.25
Therefore, the range of the function is from $43.00 to $99.25.