Question 1193644: When you buy an ice cream sundae at a local shop, you can have up to 5 toppings at a cost of 25 cents each. If a plain sundae costs $3.50, the total cost of the sundae and toppings is C(x) = 0.25x + 3.50 . What is the range of this situation?
Answer by math_tutor2020(3816)   (Show Source):
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"you can have up to 5 toppings" tells us that 5 is the most toppings possible.
On the other side, 0 toppings is the lowest amount you can have.
The values of x span from x = 0 to x = 5, where x is an integer representing the number of toppings.
C(x) is the cost based on what you pick for x.
If x = 0, then,
C(x) = 0.25x + 3.50
C(0) = 0.25(0) + 3.50
C(0) = 3.50
It costs $3.50 if you don't pick any toppings.
If you pick x = 1 topping, then,
C(x) = 0.25x + 3.50
C(1) = 0.25(1) + 3.50
C(1) = 3.75
The cost is now $3.75; basically we added on 25 cents to get this new price.
Repeat for x = 2, x = 3, x = 4 and x = 5 to get these costs
C(2) = 4.00
C(3) = 4.25
C(4) = 4.50
C(4) = 4.75
Each C(x) output is an element of the range.
Answer: The range is {3.50, 3.75, 4.00, 4.25, 4.50, 4.75}
Don't forget to use curly braces to tell the reader the range is a set of values. It's the set of all possible outputs of a function.
It's a finite and discrete set because x could only take on the values from {0,1,2,3,4,5}; in other words, we can't pick x = 1.5 since we can't select half a topping. Therefore, the domain is also finite and discrete.
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