Question

Taylor buys nail polish from a shop that cost $3.95 each. She has a maximum of $30 to spend on nail polish purchases. The total cost, with respect to polishes purchased, can be modeled by a function. Which statement correctly defines the domain of the function?

The domain is the set of all whole numbers greater than or equal to 0 and less than or equal to 8.
The domain is the set of all whole numbers greater than or equal to 0 and less than or equal to 27.65.
The domain is the set of all whole numbers greater than or equal to 0 and less than or equal to 7.
The domain is the set of all whole numbers greater than or equal to 0 and less than or equal to 30.

Answer 1

The domain is the set of all whole numbers greater than or equal to 0 and less than or equal to 7.

Explanation:

let x be the number of nail polishes that Taylor purchases .

Therefore the amount spent by Taylor on nail polishes will be f(x) = 3.95\times x

since Taylor has only 30 dollars to spend on nail polishes.

f(x) \leq 30 dollars

therefore 3.95\times x \leq 30

x \leq 7.594

since x is an whole number x = 7

Therefore the domain is the set of all whole numbers greater than or equal to 0 and less than or equal to 7.