# How do you graph y=1/(x-2)?

Jan 27, 2017

Explanation below.

#### Explanation:

Let $f \left(x\right) = \frac{1}{x}$ and $g \left(x\right) = \frac{1}{x - 2}$. Then the graph of $f$ is:

graph{1/x [-10, 10, -5, 5]}

Notice that $g \left(x\right) = f \left(x - 2\right)$. This means that to get the graph of $g$, shift the graph of $f$, $2$ units to the right:

graph{1/(x-2) [-10, 10, -5, 5]}

In general, if $A$ and $B$ are two functions of $x$, and

$B \left(x\right) = A \left(x - k\right) + m$,

then the graph of $B$ is the graph of $A$ shifted

$k$ units to the right, and $m$ units upwards.

If $k$ is negative, shift to the left instead.

If $m$ is negative, shift downwards.

(The above hold with respect to the above equation.)