You buy x bottles of soda for $1.50 using a gift card that you got as a reward for getting good grades
on your last report card. your gift card's original balance was $15. the function f(x) = $15-$1.50
represents the amount of money you have left on the card after your purchase. what is the domain of
the function? explain your reasoning.

Step-by-step explanation:

The function is    where x is the number of bottles of soda.

The domain means the set of "allowed" x values.

Also, f(x) means the amount of money left, which cannot be less than 0. So we put 0 into f(x) and solve for x:

This means the highest number of bottles you can buy is 10. So the domain is anything from 0 to 10. You can buy 0 until highest 10 bottles. Hence the domain is

f(x) = x^3 -2x^2 -3x

x( x^2 -2x-3)

x( x^2 +x -3x -3)

x( x(x+1) -3(x+1))

x( x-3)( x+1)

so zeroes are 0, 3,-1

its (2) option