Question

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

Answer 1

Explanation below.

Explanation:

Let `f(x) = 1/x` and `g(x) = 1/(x-2)`. Then the graph of `f` is:

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

Notice that `g(x) = f(x - 2)`. 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(x) = A(x - k) + 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.)