Question

If G (x) = 1/x were shifted 2 untold to the left and 2 united up, what would the new equation be?

Answer 1

Horizontal translation are obtained by the following transformation:

`f(x)\mapsto f(x+k)`

In particular, you translate k units to the left if k>0, k units to the right if k<0.

Similarly, vertical translation are obtained by the following transformation:

`f(x)\mapsto f(x)+k`

In particular, you translate k units up if k>0, k units down if k<0.

So, you proceed like this: start with

`G(x)=(1)/(x)`

Translate 2 units to the left:

`G(x+2) = (1)/(x+2)`

Translate 2 units up:

`G(x+2)+2 = (1)/(x+2)+2`