2. Exponential functions
A function in which x is in the power is called an exponential function.
Exponent is another name for power.
The general form is:
y = b(ax)
where a and b are constants and a is positive.
The graph of an exponential function is called an exponential curve.
An asymptote is a line that a curve approaches, but never touches.

3. Example 1 y = 10x y = 3x y = 2x Sketch the following curves y = 2x x-3 -2 -1 1 2 3 y
1/8 1 2 4 8
y = 3x x -3 -2 -1 1 2 3 y 1 3 9 27
All curves of the form ax pass through the point (0,1)
0·037
0·11
0·33
Also sketched is 10x and 1·4x.
As the value of a gets bigger the curve gets:
steeper to the right of the y-axis and
closer to x-axis to the left of the y-axis.
The x-axis is an asymptote.
y = 1·4x

4. Example 2 y = 3(2x) Sketch the following curves y = 2x y = 0·3(2x) x-3 -2 -1 1 2 3 y
0·04
0·08
0·15
0·3
0·6
1·2
2·4
y = 3(2x) x -3 -2 -1 1 2 3 y
3/8 1½ 3 6 12 24
Also sketched is 2x.
As the value of b gets bigger in y = b(ax):
the curve gets steeper
The curve cuts the y-axis at b instead of 1.
y = 0·3(2x)

5. Example 3 Today’s work y = 1·2(2x) x -3 -2 -1 1 2 3 y -0·3 -0·6 -1·21 2 3 y
-0·3
-0·6
-1·2
-2·4
-4·8
As b is negative
the curve is upside down
As b is 1·2
the curve cuts the y-axis at 1·2
-0·15
-9·6
Today’s work
Exercise 12 D page 371
#6, 9, 10, 11