the linear function c=50x represents the cost in dollars of each customer can buy from zero to 4 what is the domain

Question

I am learning how to solve these but they don't make sense, can you help?

Answer 1

A function has a domain and a range.

   domain - the allowable values for the input variable (usually called the x-values); x is the independent variable.

   range - the allowable values for the output variable (usually called the y-values); y is the dependent variable.

 

This problem should say, "The linear function c=50x represents the cost in dollars that a number of customers, from 0 to 4, can buy.  What is the domain?"  PLZ read this wording carefully.

 

The independent variable, x, is the number of customers.  The number of customers can have values from 0 to 4 (whole integers, of course, since it represents people -- 0, 1, 2, 3, 4).

 

The dependent variable, y, is the cost in dollars for the products.  The allowable values are ... (oh, that's the domain, which is what the problem asks us to find; so, let's find it.)

 

    Domain                                  Range

         x                                         y

   Number of Customers              Cost

---------------------------         ---------------

        0                                         0

        1                                        $50

        2                                       $100

        3                                       $150

        4                                       $200

 

So, the range goes from $0 to $200 (and includes only the value listed above).  This means that if you look at a receipt for 0.8 or 00,8 customers, it must be pretty silly (sorry, Kelsie C.).  See this article about "laugh and move on:"

 

  http://blog.codinghorror.com/the-ten-commandments-of-egoless-programming/

Answer 2

Domain refers to the maximum and minimum x-values within a given function. In this problem, you are given the range (y-values) 0 to 4, and the function that accompanies them. Since this is a positive linear function, we know that as x increases, y increases, and vice versa. That means that the smallest x value will occur at the same place that the smallest y value occurs. We can use this to find the domain.

 

In this case, they have used a c instead of a y, but it represents the same thing, the range. If we plug in the smallest range value, 0, for c, we can solve for the smallest domain value:

 

c = 50x      (Plug in 0 for c)

0 = 50x      (Divide both sides by 50)

0 = x

 

So now we know that the smallest x value is 0.

Now let's plug in the highest range value for c:

 

c = 50x      (Plug in 4 for c)

4 = 50x      (Divide both sides by 50)

0.08 = x

 

Now we know that the highest x value is 00.8.

 

This makes sense if we consider that the slope of this function is 50. That means that for every 1 unit of x that increases, c increases by 50 units. So if the c value is anything less than 50, x will be less than 1.

 

So now that we have determined that the smallest x value is 0, and the largest is 0.08, we can say that the domain is 0 to 0.08.

 

Hope this helps!