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Graphs of Reciprocal Functions

In this lesson, we shall study graphs of reciprocal functions.

There are several forms of reciprocal functions. One of them has the form y = , where k is a real number and x ≠ 0.

Example:

Draw the graph of y = for values between –4 and 4, except for x = 0.

Solution:

x	0.2	0.5	1	2	3	4	5
y	25	10	5	2.5		1.25	1

x	–0.2	–0.5	–1	–2	–3	–4	–5
y	–25	–10	–5	–2.5	–	–1.25	–1

The curve consists of two separate pieces, but they should be regarded as one graph.

The graph gets closer to the x-axis as the value of x increases, but it never meets the axis. Each piece of the graph also gets closer to the y-axis as x gets closer to 0 but it never meets the y-axis because there is no value for y when x = 0. This type of curve is called a rectangular hyperbola.

Note that this type of curve, the graphs of y = where k is a real number and x ≠ 0, has two lines of symmetry: y = x and y = –x.

Another form of reciprocal functions is y = , where k is a real number and x ≠ 0.

Example:

Draw the graph of y = for –4 ≤ x ≤4 and x ≠ 0.

Solution:

x	–4	–3	–2	–1	–0.8	0.8	1	2	3	4
y	0.19	0.33	0.75	3	4.69	4.69	3	0.75	0.33	0.19

Notice that graphs of y = where k is a real number and x ≠ 0, has an axis of symmetry on the y-axis (i.e. x = 0)

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