Question

Alan has $400 in his checking account. He withdraws $50 each week. The amount remaining in his account, f(x), after x weeks is

represented by a function. What is the range of the function?

Answer 1

{0, 50, 100, 150, ..., 350, 400}

Explanation:

The range of Alan's balance will be multiples of 50 that are between (and including) 0 and 400.

{0, 50, 100, 150, ..., 350, 400}

_____

The expression for f(x) is ...

f(x) = initial balance - (rate of withdrawal) × (time period)

f(x) = 400 -50x

This is a continuous linear function defined for all x, and capable of producing f(x) values between -∞ and +∞. The range of this function is "all real numbers."

However, as applied to this problem, the domain of x is the set of integers from 0 to 8. The corresponding range is multiples of 50 from 0 to 8, that is, values 0, 50, ..., 350, 400.