Question

The graph of g(x) contains the point (7,12). What point must be on the graph of the function f(x) if g(x) = 2f(x-3)+4?

Answer 1

First take out 2 as a factor
g(x) = 2[f(x-3)+2]


f(x-3) means a shift of +3 in the x direction
+2    means a shift of +2 in the y direction
2[f]   means a stretch of scale factor 2 in the y direction

so (7+3, 2(12+2)) -> (10,28)