1. Exponential Functions and Their Graphs
Sec. 5.1
Exponential Functions and Their Graphs

2. Algebraic Functions
Polynomial functions and rational functions

3. Transcendental functions
Exponential functions and logarithmic functions

4. Definition of Exponential Function
f(x) = ax a > 0, a ≠ 1, and x is a real number
a is the base
x is the exponent

5. Natural Base Represented by e e ≈ 2.71828… (Irrational)
f(x) = ex is called the Natural Exponential Function

6. Ex. 1
2-3.1
2-π

7. Ex. 2 Evaluate and round to nearest thousandth
3.92.1
2-3π
4√5291

8. Ex. 5
a) e-2
b) e-1
c) e1
d) e2

9. Graph of Exponential Functions
f(x) = 2x
g(x) = 4x x 2x 4x -2 -1 1 2 3

10. F(x) = 2-x
G(x) = 4-x x
2-x
4-x -3 -2 -1 1 2

11. Note: the negative exponent reflects about the y-axis
Find for each
Domain
Range
Intercept
Direction
Horizontal Asymptote
Continuous?

12. Graph on the calculator
h(x) = (½)x
It is the same as f(x) = 2-x

13. What will happen to the graph of f(x) = 2x
Which means 2x+2
f(x-3)
f(x) + 3
Which means 2x + 3
f(x) – 2
-f(x)

14. Summary Given f(x) = ax f(-x) = a-x f(x+b) = ax+b f(x-b) = ax-b
Reflects about y axis
Horizontal left b units
Horz. Right b units
Vertical up b units
Vertical down b units
Reflects over x axis