The function g (x) = (x-2^2. The function f (x) = g (x) + 3

The function f (x) is shifted horizontally how many places to where?

The function f (x) is shifted vertically how many places where?

The parent function is:

y = x ^ 2

Applying the following function transformation we have:

Horizontal translations:

Suppose that h> 0

To graph y = f (x-h), move the graph of h units to the right.

We have then:

g (x) = (x-2) ^ 2

Then, we have the following function transformation:

Vertical translations

Suppose that k> 0

To graph y = f (x) + k, move the graph of k units up.

We have then that the original function is:

g (x) = (x-2) ^ 2

Applying the transformation we have

f (x) = g (x) + 3

f (x) = (x-2) ^ 2 + 3

Answer:

the function f (x) moves horizontally 2 units rigth.

The function f (x) is shifted vertically 3 units up.