4.3 Exponential Functions
What is the longest running game show?
Laws of Exponents - Review
Exponential Functions
An exponential function is a function of the form:
f ( x)  b x
where a is a positive real number (b > 0) and b ≠ 1.
f (x)  2x
x
f (x)  (1 2) x
y
x
ff (x)
(x) == 22xx
 f (x) = 5x
y
f (x) = (1/2)xx
f (x) = (1/5)x
Properties of Exponential Functions
f ( x)  b ,b  1
x
Domain/Range
Intercepts
Asymptotes
Inc or Dec
Domain: (-∞,∞)
x-int: None
y = 0 as x
-∞
f ( x)  b ,0  b  1
x
Range: (0,∞)
y-int: (0,1)
y = 0 as x
∞
Increasing and 1-to-1 Decreasing and 1-to-1
Common Points
Other
Graph is smooth/continuous (no corners/gaps)
Exponential Transformations
Determine the equation for each graph using transformations
of the function y = 5x.
1)
2)
y = 5x
3)
4)
Exponential Transformations
Determine the equation for each graph using transformations
of the function y = 5x.
5)
6)
7)
8)
Exponential Equations
2x 1
a) Solve : 3
1

81
If a  a , then u  v
u

v
Exponential Equations
If au  av , then u  v
2
b) Solve : 4 x  2x

Exponential Equations
c) Solve : e

4 x
If au  av , then u  v
2
 e x  e12

Group Challenge! (1/2 Sheet)
x 1
2
x
x
1) Solve : 8  4 
32
If au  av , then u  v

x
1



16
2) Solve : 27  4
22 x 1
4.3 Exponential Functions
Homework #14: p.284
#29-36, 53-65 odd, 71-74, 75, 77