Albert Teen
powered by
Albert logo

YOU ARE LEARNING:

pointer
Reciprocal Graphs
lessonMenuButton

Reciprocal Graphs

lesson introduction

Reciprocal Graphs

Reciprocal graphs contain x as the denominator of a fraction, and have a very distinct symmetrical shape.

Reciprocal graphs describe functions which contain xx in the denominator. They have a distinctive shape with two separate lines which are symmetrical to each other.

1

It is symmetrical about the line y=xy=x

Look at the graph above to see this illustrated.

block image

Let's now find some points for the curve y=6xy=\frac{6}{x}

1

To do this, we substitute into the equation values for xx

and then calculate the corresponding value of yy.

block image
2

What will yy equal to when x=2x=2 ?

hint button
block image
3

So when x=2x=2, y=3y=3

We can now plot this point (2,3)(2, 3) on the graph.

block image
4

What is y=6xy=\frac{6}{x} when x=1x=1 ?

hint button
block image
5

So when x=1x=1, y=6y=6

We can now plot this point (1,6)(1,6) on the graph.

block image
6

What will yy be equal to when x=6x=6 ?

hint button
block image
7

Will the curve y=6xy=\frac{6}{x} pass through the origin, (0,0)(0,0) ?

hint button
block image
8

We know that the curve will not touch either of the axes so we can join these points up, and continue the line so that it runs along the axes with touching them.

This gives us half of the graph. There is also another curve in the opposite quadrant to be drawn.

block image
9

To find the other half, we can simply mirror the points along the line y=-x.

This is the same as making all of the points negative.

block image