Exploring the Properties of Exponential Functions
Graph y = 2x and y = ( 12 ) using a table of values. Plot each set of
ordered pairs and draw a smooth curve through the points. What do
you notice?
x
x
-3
-2
-1
0
1
2
3
y
x
-3
-2
-1
0
1
2
3
y
y
8
6
4
2
-6
-4
-2
What do you notice about these two graphs?
Identify the asymptote.
x
0
0
-2
2
4
6
Graph y = 3x and y = ( 13 ) .
x
x
-3
-2
-1
0
1
2
3
y
y
8
6
4
2
x
-3
-2
-1
0
1
2
3
y
-6
-4
-2
0
-2
What do you notice about these two graphs?
Identify the asymptote.
x
0
2
4
6
Graph y = ( 32 ) , and y = ( 23 ) .
x
x
-3
-2
-1
0
1
2
3
x
-3
-2
-1
0
1
2
3
x
y
y
8
6
4
2
y
-6
-4
-2
What do you notice about these two graphs?
Identify the asymptote.
x
0
0
-2
2
4
6
Key Ideas
•
•
•
•
•
•
All pass through the point (0, 1)
All have horizontal asymptotes at y = 0
If base >1, the graph represents exponential growth
If 0<base<1, the graph represents exponential decay
Domain:
Range: y   | y  0
NOTE:
y = 0x
y=0
Not an exponential function.
y = 1x
y=1
Not an exponential function.