Question

The function f(x) is shown in the table.

-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)?.
Use the drop-down menus to compare the y-intercepts of f(x) and g (x).
lick the arrows to choose an answer from each menu.
The y-intercept of f(x) is Choose...
The y-intercept of f(x) is Choose...
and the y-intercept of g (x) is Choose...
• the y intercept of g (x).

Answer 1

To find the y-intercepts of the functions \( f(x) \) and \( g(x) \):

1. **For \( f(x) \)**: The y-intercept occurs when \( x = 0 \). From the table provided:
- At \( x = 0 \), \( f(0) = -6 \).

2. **For \( g(x) \)**: The function is given as \( g(x) = 2(x - 2)^2 \). To find the y-intercept, we substitute \( x = 0 \):
\[
g(0) = 2(0 - 2)^2 = 2(-2)^2 = 2(4) = 8.
\]

Now we can fill in the drop-down menus:

- The y-intercept of \( f(x) \) is \( -6 \).
- The y-intercept of \( g(x) \) is \( 8 \).

So, comparing the two:
- The y-intercept of \( f(x) \) is less than the y-intercept of \( g(x) \).

Fill-in responses:
- The y-intercept of \( f(x) \) is **-6**.
- The y-intercept of \( g(x) \) is **8**.
- And the relationship is that the y-intercept of \( f(x) \) is **less than** the y-intercept of \( g(x) \).