Question

Suppose the g(x)=f(x+8)+4. Which statement best compare the graph of g(x) with the graph of f(x)?

Answer 1

In the translation of graph,
the image is
g(x)=f(x-h)+k
where
h=translation to the right
k=translation upwards.

For the given transformation,
g(x)=f(x-(-8))+4
we see that h=-8, k=+4
so we conclude that g(x) is a translation of f(x) 8 units to the left, and 4 units up.