Find the value that completes the ordered pair to describe the transformation of f(x) to g (x). If (x, y) is a point on f(x), then

(x +
3
, y +
1
) is a point on g(x).

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.