Week 13 – Reciprocal Linear Functions

The reciprocal is when 1 is divided by the number or function.

For example:

The reciprocal function of y = 5x – 2 is 

The graph of  y = 5x – 2 looks like this:

The graph of  looks like this:

This is called a hyperbola.

The points (0.2, -1) and (0.6, 1) are both common on the graph. They are called invariant points.

The blue dotted line is the vertical asymptote where x = 0.4 and the horizontal asymptote will always be y = 0 since it goes right through the x-axis.

To find the points of the hyperbola, take the reciprocal of the y-value from the linear graph. For example, the point (0, -2) would be (0, 1/-2). Then join the points with a curve. It should come close to the asymptotes but never touch them.