Answer:
r(x) = f(x +4) +2
Step-by-step explanation:
You want the function that transforms f(x) so that it passes through the point (-2, 5).
Vertex
We notice the vertex of the function f(x) is (2, 3). To move the vertex to (-2, 5), we need to translate it left 4 units and up 2 units.
Transformation
Translating f(x) by (right, up) = (h, k) makes the equation look like ...
g(x) = f(x -h) +k
Here, we want h = -4, k = +2, so we're looking for a match to ...
g(x) = f(x -(-4)) +2 = f(x +4) +2
This form matches r(x) = f(x +4) +2.
