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

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Answer 1 · 2017-01-27T19:13:21

Explanation below.

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.)