Question

Zach plans to save $25 a week to purchase a new bike. The function f(x) = 250 - 25x models the amount of money Zach will need to purchase the bike x weeks after he starts saving. Which is the most appropriate domain for the function?

A) All integers less than or equal to 10

B) All integers greater than or equal to 10

C) All non-negative integers less than or equal to 10

D) All non-negative integers greater than or equal to 10

Answer 1

The most appropriate domain for the function f(x) = 250 - 25x is all non-negative integers greater than or equal to 10.

Step-by-step explanation:

The most appropriate domain for the function f(x) = 250 - 25x is option D) All non-negative integers greater than or equal to 10.

The function models the amount of money Zach will need to purchase the bike x weeks after he starts saving. Since Zach plans to save $25 a week, the function represents the amount of money needed to purchase the bike after x weeks by subtracting 25 times the number of weeks from 250.

In order for the function to make sense, x should be a non-negative integer, meaning it can't be a negative number or a fraction. Furthermore, since Zach plans to start saving, the number of weeks should be greater than or equal to 0. Since the question states that the function is valid for 0 ≤ x ≤ 20, the most appropriate domain is all non-negative integers greater than or equal to 10, which includes the values of x within this range.