COMPLETE QUESTION:
Andrea is selling candles as a fundraiser. She spent $50 on supplies for making the candles. She plans to sell the candles for $10 each. Her profit can be modeled by C(x) = 10x - 50.
What type of function is this?
What is the domain and range of the function?
Answer:
- This function is one-to-one
- Domain D = {x: x is a whole number ≤ Z}
- Range R = {y: y is in -50, ..., (10Z - 50)}
Where Z is the number of candles she could produce with $50.
Step-by-step explanation:
Given that her profit is modeled by C(x) = 10x - 50
- This function is one-to-one, because it is in the form f(x) = y.
Let the number of candles she could make with $50 be Z.
Then the domain is the set of all whole numbers less or equal to Z.
D = {x: x is a whole number ≤ Z}
If there are infinite number of candles she could make with that money, then
D = (-infinity, infinity)
When x = 0, we have C = -50
When x = Z, we have C = 10Z - 50
The range is then given as
R = whole numbers from -50 up to (10Z - 50)
R = {y: y is in (50 -Z), ..., (10Z - 50)}
If there are infinite number of candles she could make with that money, then
R = (-infinity, infinity)
:D