Exponential functions

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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.
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Example 1
y 2x
y 3x
y 10x
Sketch the following curves
y 2x
x -3 -2 -1 0 1 2 3
y
1/8
¼
½
1
2
4
8
y 3x
x -3 -2 -1 0 1 2 3
y
1
3
9
27
011
033
0037

• Also sketched is 10x and 14x.
• 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 14x
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Example 2
y 3(2x)
y 2x
Sketch the following curves
y 03(2x)
x -3 -2 -1 0 1 2 3
y
03
06
12
24
004
008
015
y 3(2x)
x -3 -2 -1 0 1 2 3
y
3/8
¾
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 03(2x)
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Todays work
Example 3
y ?12(2x)
x -3 -2 -1 0 1 2 3
y
-12
-24
-48
-06
-03
As b is negative the curve is upside down As b is
?12 the curve cuts the y-axis at ?12
-96
-015
Exercise 12 D page 371 6, 9, 10, 11