Hyperbolic function

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 cant 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 0 ¼ ½ 1 2 4
y
X
4
2
1
½
¼
-4
-2
-1
-½
-¼
y 2/x
x -4 -2 -1 -½ - ¼ 0 ¼ ½ 1 2 4
y
X
8
4
2
1
½
-8
-4
-2
-1
-½
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 0 ¼ ½ 1 2 4
y
X
-4
-2
-1
-½
-¼
4
2
1
½
¼
y ?4/x
x -8 -4 -2 -1 -½ 0 ½ 1 2 4 8
y
X
-8
-4
-2
-1
-½
8
4
2
1
½
If a is negative the hyperbola is in the 2nd and
4th quadrants.
4
Todays work
Exercise 12D pg 372 4, 7, 8