Question

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 ?

Answer 1

The function f(x) moves horizontally 2 units right.

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

Explanation:

Answer 2

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.