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

$G(x)=\dfrac{1}{x}$

Translate 2 units to the left:

$G(x+2) = \dfrac{1}{x+2}$

Translate 2 units up:

$G(x+2)+2 = \dfrac{1}{x+2}+2$