Find the function g that is finally graphed after the following transformations are applied..?

Question

in the order given to the graph of a

function f:

(1) reflect about the x-axis;

(2) shift down 3 units;

(3) stretch vertically by a factor 7;

(4) reflect about the y-axis.

Answer 1

Start with f(x).

1.  Reflected about the x-axis causes it to be -f(x).

2.  Shifted down by 3, it becomes -f(x) - 3.

3.  Stretched by a vertical factor of 7, it becomes 7[-f(x) - 3] = -7f(x)-21.

4.  Reflected about the y-axis, it becomes -7f(-x) - 21.

Answer: -7f(-x) - 21