A costume designer will buy between 5 and 12 hats for the actors in a play. Each hat costs $7. The function c(h) = 7h models the total amount of money the costu

Question

Im trying to figure out how to get this equation and the answer im so confused!!

answers are

What is the practical range of the function?

all real numbers from 5 to 12, inclusive

all real numbers from 35 to 84, inclusive

all integers from 5 to 12, inclusive

all multiples of 7 between 35 and 84, inclusive

Answer 1

A function is a  mapping or one value (indicated by the independent variable) to another variable (indicated by the dependent variable).  The mapping produces, at most, one output for each input.  Those conditions make it a function.

 

In this problem, the number of hats purchased is the independent variable.

 

The amount of money the costumes cost is the dependent variable (because it "depends" on the number of hats purchased).

 

Domain: The domain of a function is the set of all possible input values (often the "x" variable), which produce a valid output from a particular function. It is the set of all real numbers for which a function is mathematically defined.

 

Range: The range is the set of all possible output values (usually the variable y, or sometimes expressed as f(x)), which result from using a particular function.

 

In this problem, the domain of the function is "between 5 and 12 hats."    (integers between 5 and 12)

 

We calculate:   (number of hats)*(cost per hat) = cost                 [number of hats cancels out, leaving only cost]

 

So, the range includes the numbers 35, 42, 49, 56, 63, 70, 77, and 84.     Only those integers!

 

 

 

Answer 2

Hi Bob:

 

So, to answer your question...all multiples of 7 between 35 and 84 is the practical range of the function and this is why:

 

• the function c(h) = 7h reads as "c of h equals 7 times h."
• This function is referring to the total cost of hats dependent upon the number purchased where c(h) or "cost of hats" is the dependent/output variable, and h is the number of hats purchased which is the independent/input variables.
• The range of a function refers to the range of dependent/output (The Y-axis if you will).  The range here is all multiples of 7 between 35 and 84 because the costume designer may purchase (independent) between 5 and 12 hats, which would cost anywhere from $35 to $84, all multiples of $7, depending upon amount of hats purchased.
• The domain of a function refers to the range of independent/inputs of the function (The X-axis range if you will),  Here your domain is all integers, 5 to 12, and integers because all real numbers includes fractions, but you are only purchasing units of hats, not fractions.

 

Bob, I hope this explains the question clearly, please feel free to contact me if you have any questions or need any tutoring assistance.

 

Thanks,

Jason

Answer 3

The least number of hats is 5 and the cost is 5($7) or $35

The most number of hats is 12 and the cost is 12($7) or $84.

 

Not matter how many hats he buys, the cost is a multiple of 7 (each hat costs $7)

 

all multiples of 7 between 35 and 84 inclusive