1. Graph of Exponential Functions
Chapter 3
Lesson G

2. Exponential Functions
The general exponential function has form f(x) = a^x where a>0, a≠1
y=0 is a horizontal asymptote

3. Example
Graph y= 2^x

4. General Exponential Function
y= a x b ^(x-c) +d
b controls how steeply the graph increases or decreases
c controls horizontal translation
D controls vertical translation and y=d is the equation of the horizontal asymptote

5. General Exponential Function
If a>0, b>1
If a>0, 0<b<1
If a<0, b>1
If a<0, 0<b<1

6. Horizontal Asymptotes
y= a x b ^(x-c) +d
In this function y=d is the horizontal asymptote
Using these you can obtain a reasonably accurate sketch of the graph
Horizontal asymptote
Y-intercept
Two other points, say when x=2, x=-2

7. Example

8. Homework
Page #1-5