Question

consider the table for f(x) and the graph for g(x). which statement is true when comparing the y-intercepts of the functions?
a the y-intercept for f(x) is greater than the y-intercept for g(x).
b the y-intercept for both functions is (0, 0).
c the y-intercept for g(x) is greater than the y-intercept for f(x)
d the y-intercept for both functions is (0, 2).

Explanation:

Step1: Find y-intercept of \( f(x) \)

The y-intercept occurs at \( x = 0 \). From the table, when \( x = 0 \), \( f(0)=2 \). So the y-intercept of \( f(x) \) is \( (0, 2) \).

Step2: Find y-intercept of \( g(x) \)

The y-intercept of a graph is where it crosses the y - axis (when \( x = 0 \)). From the graph of \( g(x) \), when \( x = 0 \), the y - value is 1 (by looking at the point where the graph intersects the y - axis).

Step3: Compare the y-intercepts

The y-intercept of \( f(x) \) is 2 and the y-intercept of \( g(x) \) is 1. So \( 2>1 \), meaning the y-intercept of \( f(x) \) is greater than that of \( g(x) \).

Answer:

A. The y - intercept for \( f(x) \) is greater than the y - intercept for \( g(x) \)