This document discusses exponential functions and graphs. It provides examples of exponential growth and decay functions, shows how to write exponential functions based on patterns in tables, and how to graph exponential functions. Key aspects of exponential functions covered are their domains of all real numbers, ranges of positive values for growth and negative values for decay, and how the base affects whether the graph is a vertical stretch or shrink. Sample homework problems are also presented on graphing and analyzing exponential decay functions.

1. Exponential
Functions & Graphs
Algebra 1
February 21, 2013

2. Linear vs. Exponential
Linear Exponential
+1 +1 +1 +1 +1 +1
x -1 0 1 2 x -1 0 1 2
y 2 4 6 8 y 2 4 8 16
+2 +2 +2 •2 •2 •2
y = 4 ( 2)
x
y = 2x + 4

3. Writing Exponential Functions
Write the rule for the functions.
+1 +1 +1 +1 +1 +1
x -1 0 1 2 x -1 0 1 2
y 1 3 9 27 y 6 3 1.5 0.75
• 3 •3 •3 • 0.5 • 0.5 • 0.5
y = 3( 0.5)
x
y = 3(3)
x
Exponential Growth Exponential Decay

4. Graphing Exponential Functions
x -4 -3 -2 -1 0 1 2 3 4
y= 2x y 1/16 1/8 1/4 1/2 1 2 4 8 16
Use colored pencil
x -4 -3 -2 -1 0 1 2 3 4
y= (½)x y 16 8 4 2 1 1/2 1/4 1/8 1/16
Use different colored pencil

5. • •
Exponential Exponential
Decay Growth
• •
• •
y= 2x
• • • • • • •
Domain: all real numbers
Range: y > 0
y = (½)x
Domain: all real numbers
Range: y > 0

6. y = 2x
Domain: all real numbers • •
Range: y > 0
• • •
y= 2(2)x
• • •
• • • • •
Domain: all real numbers
• • • •
•
Range: y > 0
|a| > 1  vertical stretch
y = ¼ (2)x
Domain: all real numbers
Range: y > 0
0 < |a| < 1  vertical shrink

7. y = (½)x
Domain: all real numbers •
Range: y > 0
•
y= -(½)x
•
Domain: all real numbers • •
• •
• •
Range: y < 0 • •
•
a < 0  reflection through •
the x-axis
•

8. Sample Homework 20
Problem
y = -2(⅓)x 10
•
a) Graph the function
b) Compare the graph with the
graph of y = (⅓)x •2
• •
• reflected through x-axis -2 •
•
• vertical stretch
c) Identify the domain and range •
Domain: all real numbers -10
Range: y < 0
•
-20