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 $f(x)$

From the table, when $x=0$, $f(0)=-6$.

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

Substitute $x=0$ into $g(x)$:
$$g(0)=2(0-2)^2=2\times(-2)^2=2\times4=8$$

Step3: Compare the two values

$-6 < 8$, so the y-intercept of $f(x)$ is less than that of $g(x)$.

Answer:

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