naming new points in transformations of linear equations

Question

Use the transformation to identify the new point.

g(x) = f(x-8) + 5

original point: (-4, 12)

answer key says new point is (4, 17)

I think new point is (-4, -7)

Please help!

Answer 1

Replacing x by x-8 in f(x) translates the graph of y = f(x) 8 units to the right. So, (-4, 12) moves to (4, 12). Then shift upward 5 units to get (4, 17).