Question

the function f(x) is shown in the table.
x | -4 | -2 | 0 | 2 | 4
f(x) | -18 | -12 | -6 | 0 | 6
the function g(x) is represented by the equation g(x) = 2(x - 2)².
use the drop - down menus to compare the y - intercepts of f(x) and g(x).
click the arrows to choose an answer from each menu.
the y - intercept of f(x) is choose... and the y - intercept of g(x) is choose...
the y - intercept of f(x) is choose... the y - intercept of g(x).

Explanation:

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

The y-intercept occurs at \( x = 0 \). From the table of \( f(x) \), when \( x = 0 \), \( f(0)= -6 \). So the y-intercept of \( f(x) \) is \( -6 \).

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

For a function \( g(x) \), the y-intercept is found by setting \( x = 0 \) in \( g(x)=2(x - 2)^2 \). Substitute \( x = 0 \): \( g(0)=2(0 - 2)^2=2\times(- 2)^2=2\times4 = 8 \). So the y-intercept of \( g(x) \) is \( 8 \).

Step3: Compare the y-intercepts

Compare \( -6 \) and \( 8 \). We know that \( -6<8 \).

Answer:

The y - intercept of \( f(x) \) is \( -6 \) and the y - intercept of \( g(x) \) is \( 8 \). The y - intercept of \( f(x) \) is less than the y - intercept of \( g(x) \).