Answer:
we know that if: (x, y) is a point of f(x):
This means that f(x) = y.
Then (x + 3, y + 1) is a point of g(x)
This means that:
g(x + 3) = y + 1
Then we have two shifts.
For a real and positive number A.
A horizontal shift of A units to the right can be written as:
f(x - A)
A vertical shift of A units up can be written as:
f(x) + A.
Then in this case we have:
An horiozontal shift of 3 units to the right, and a vertical shift of 1 unit up, this means that:
g(x') = f(x' - 3) + 1.
then evaluating this at x' = x + 3
g(x + 3) = f(x + 3 - 3) + 1 = f(x) + 1 = y + 1
That is what we had initially.
