Question

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

f(x) = x-?
g(x) = (x + 5)2 + 2
g(x) = (x + 2)2 + 5
g(x) = (x - 2)2 + 5
g(x) = (x – 5)2 + 2
UT

Answer 1

Answer: Last option.

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`