Question

The graph of the function f(x) = -1/x is centered at the origin as shown on the left below. The graph on the right is the same graph translated so that it is centered at (-2,2). Write the equation of the graph on the right.

Answer 1

To translate f(x) to (-2, 2) you replace x by x-(-2), and you replace f(x) by f(x)+2.

Doing both these things, the equation becomes

... y = f(x+2)+2

... y = -1/(x+2) +2