Question

Describe how the graph of the function y = f(x-3) can be obtained from the graph of y = f(x).

Answer 1

Any graph f(x) can be changed to f(x-3) by changing any x to x-3.

For example:  Let f(x) = x^{2} + 2x + 4

Find f(x-3) by replacing all x's with x-3.

f(x-3) = (x - 3)^{2} + 2(x - 3) + 4

Then we can simplify and we will have f(x-3).