Question

Suppose f(x) =x^2. Find the graph of f(x+3)

Answer 1

You must substitute x+3 for x, so x² becomes (x+3)².

You could work this out to be x²+6x+9 if that is asked.

The graph of (x+3)² is the graph of x² shifted to the left by 3.

If this seems counterintuitive, think of the value you must choose for x to make the outcome 0. It used to be 0²=0, but now it is -3 since (-3+3)²=0, so 3 positions to the left.