Question

What is the equation of the translated function, g(x), if

Answer 1

Answer: Last option.

Step-by-step explanation:

The complete question is: "What is the equation of the translated function, $g(x)$ if $f(x) = x^2$?

The missing graph is attached.

Below are shown some transformations for a function $f(x)$ :

1. If  $f(x)+k$ the function is translated "k" units up.

2. If  $f(x)-k$ the function is translated "k" units down.

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

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

In this case, you can observe in the graph that the vertex of the parabola (function $f(x)$) is at the following point:

 $(0,0)$

And the vertex of the translated parabola (function $g(x)$) is at this point:

$(5,2)$

Therefore, based on the transformations explained before, you can identify that the function $g(x)$ is obtained by translating the function $f(x)$ 5 units to the right and 2 units up.

Then, the equation of the function $g(x)$ is:

$g(x)=(x-5)^2+2$