1. Hyperbolic function The general form of a hyperbolic function is:
y = a/x or xy = a
where a is a constant.
As x is in the denominator, as x gets larger, y gets smaller.
As x gets smaller, y gets larger.
The graph of a hyperbolic function is called a hyperbola.
A hyperbola is of the form y = a/x is symmetrical about the origin.
Note:
You can’t divide by zero,
The x and y-axis are asymptotes,
Point symmetry means you can rotate a curve 180º and it is the same.

2. Example 1 y = 1/x y = 2/x Sketch the following y = 1/x x -4 -2 -1 -½
- ¼ 1 2 4 y -¼ -½ -1 -2 -4 X 4 2 1
y = 2/x x -4 -2 -1 -½
- ¼ 1 2 4 y -½ -1 -2 -4 -8 X 8 4 2 1
As a increases the hyperbola moves out from each axis.
The hyperbola is in the 1st and 3rd quadrants.

3. Example 2 Sketch the following y = 1/x x -4 -2 -1 -½ - ¼ ¼ ½ 1 2 4 y1 2 4 y 1 2 4 X -4 -2 -1 -½ -¼
y = 4/x x -8 -4 -2 -1 -½ 1 2 4 8 y 1 2 4 8 X -8 -4 -2 -1 -½
If a is negative the hyperbola is in the 2nd and 4th quadrants.

4. Today’s work
Exercise 12D pg 372
#4, 7, 8