Question

Which graph represents the function f (x − 3), if f (x) = x2?

Answer 1

Answer: See the graph attached.

Step-by-step explanation:

Given the Quadratic function:

$f(x)=x^2$

We can identify that it is the "Parabola parent function". The parabola passes through the origin.

There are some tranformations for a function f(x). Two of them are the following:

If $f(x+k)$, the function is shifted "k" units to the left.

If $f(x-k)$, the function is shifted "k" units to the right.

Therefore, given that:

$f (x - 3)$

We can identify that this is the function $f(x)=x^2$ but shifted 3 units to the right:

 $f (x - 3)=(x-3)^2$

Knowing this, we can conclude that the graph that represents $f (x - 3)$ is the graph attached.