Question

post test: exponential and logarithmic functions
what is the y-intercept of function g if $g(x) = -4f(x) + 12$?
a. $(0,8)$
b. $(0,12)$
c. $(0,1)$
d. $(0,-4)$

Explanation:

Step1: Find y-intercept of f(x)

The y-intercept of a function is at x = 0. From the graph, when x = 0, f(0) = 1.

Step2: Substitute into g(x) formula

Given \( g(x) = -4f(x) + 12 \), substitute x = 0:
\( g(0) = -4f(0) + 12 \)
Substitute f(0) = 1:
\( g(0) = -4(1) + 12 = -4 + 12 = 8 \)

Answer:

A. \( (0, 8) \)