Question

Functions f(x) and g(x) are shown below.
f(x) = x^2
g(x) = x^2 8x 16
In which direction and by how many units should f(x) be shifted to obtain g(x)?

Answer 1

We can factor g(x) as $(x+4)^2$.  Clearly, g(x) is simply f(x+4), so f(x) should increase each x by 4 to achieve the same result as g(x).  Therefore, f(x) should be shifted 4 units in the positive-x (or right) direction.