Question

Given the functions f(x) = -2x and g(x) = 16 - x, what can be determined about their y-intercepts?

A. The function f(x) has a higher y-intercept.
B. The function g(x) has a higher y-intercept.
C. They both have the same y-intercept.
D. The relationship between y-intercepts cannot be determined.

Answer 1

To find the y-intercepts of functions f(x) and g(x), set x to 0 and evaluate each function. Function f(x) has a y-intercept of 0, and g(x) has a higher y-intercept at 16, making B the correct answer.

Step-by-step explanation:

The y-intercepts of functions f(x) = -2x and g(x) = 16 - x can be determined by evaluating each function when x is 0. The y-intercept is the value of the function when it intersects the y-axis, which occurs when x equals 0.

For f(x), when x is 0:

• f(0) = -2(0) = 0

For g(x), when x is 0:

• g(0) = 16 - (0) = 16

Therefore, the y-intercept of function f(x) is 0, and the y-intercept of function g(x) is 16, which means that g(x) has a higher y-intercept.

The correct answer is B. The function g(x) has a higher y-intercept.