Question

If the graph of cos(2x) is translated right 3 units, what is the new function defined by

Answer 1

To translate 3 units to the right, we replace all 'x' terms with (x-3)

g(x) = f(x-3)

f(x) = cos(2x) ..... original function

f(x-3) = cos(2(x-3)) .... replace every x with (x-3)

f(x-3) = cos(2x-6) .... distribute

g(x) = cos(2x-6) is the answer

The g(x) curve is the result of shifting the f(x) curve 3 units to the right.