Question

Everything is in the picture please help asap.

Answer 1

Answer:

$f(x)=x^2$

Step-by-step explanation:

All three functions in the figure are parabolic and thus share the parent function $y=x^2$. They are horizontally dilated by some constant (unless they aren't) and can all be represented with $y=\pm ax^2$, where $a$ is some constant.

Plug in point the line passes through to find that constant. For $f(x)$, we can see the function clearly passes through (2,4):

$4=a\cdot 2^2,\\4=4a,\\a=1$

Therefore, the function of $f(x)$ is $f(x)=1x^2=\boxed{x^2}$