finding the equation based on a description

Question

Find the function g that is finally graphed after the following transformations are applied in the order given to the graph of a function f: (1) reflect about the x-axis; (2) shift down 5 units; (3) stretch vertically by a factor 7; (4) reflect about the y-axis.

Answer 1

1) reflect about the x axis tells us to substitute a -y for y. So Y = -g(x).

2) shift down 5 units Y = -g(x) -5

3) Stretch vertically by 7 Y = 7(-g(x)-5)

4) Reflect about the y-axis = substitute -x for x Y=7(-g(-x)-5)