Algebra I #5-02
Characteristics of Exponential Functions (F.IF.4)
1. Use the table function of your calculator to fill in the chart below.
f ( x)  2 x
f (x)
Function
x
-2
-1
0
1
2
3
4
Table
Base (b)
y-intercept
x-intercept
Domain
Range
Interval of increase
Interval of decrease
Horizontal Asymptote
End Behavior
Average Rate of Change
on the interval [0,3]
g ( x)  3 x
-2
-1
0
1
2
3
4
16
b = ______
2
(0,___)
1
(___,0) none
(-∞,∞)
or all real numbers
1/9
1/3
1
3
9
27
81
b = ______
3
(0,___)
1
none
(___,0)
(-∞,∞) or all real numbers
y>0
y>0
(-∞,∞)
(-∞,∞)
never decreases
0
y  ________
∞
As x   , f ( x)  ____
0
As x   , f ( x)  ____
g (x)
x
1/4
1/2
1
2
4
8
h( x)  5 x
never decreases
0
y  ________
∞
As x   , g ( x)  ____
0
As x   , g ( x)  ____
7/3
26/3
h(x)
x
1/25
1/5
1
5
25
125
625
-2
-1
0
1
2
3
4
b = ______
5
(0,___)
1
(___,0) none
(-∞,∞) or all real numbers
y>0
(-∞,∞)
never decreases
0
y  ________
∞
As x   , h( x)  ____
0
As x   , h( x)  ____
124/3
2. What happens to the table of values as b increases?
3. Did any of the characteristics stay the same? Which one(s)?
4. Did any of the characteristics change? Which one(s)?
5. Why do all of the functions contain the point (0,1)?
6. Would it ever be possible to have an exponential function of the form f ( x)  b x that does not pass through the
point (0, 1)? Why or why not?
Algebra I #5-02
Characteristics of Exponential Functions (F.IF.4)
7. Use the table function of your calculator to answer the following.
Function
Table
Base (b)
y-intercept
x-intercept
Domain
Range
Interval of increase
Interval of decrease
End Behavior
Average Rate of
Change on the
interval [0,3]
1
p ( x)   
2
x
x
1
q( x)   
 3
p(x)
-2
4
2
-1
1
0
1/2
1
1/4
2
1/8
3
1/16
4
1/2
b = ______
(0,___)
1
(___,0) none
(-∞,∞)
x
1
r ( x)   
5
x
q(x)
x
r (x)
-2
-1
0
1
2
3
4
9
-2
-1
0
1
2
3
4
25
3
1
1/3
1/9
1/27
1/81
1/3
b = ______
1
(0,___)
(___,0)
The graph is never increasing.
(-∞,∞)
As x   , p( x) 
As x   , p( x)  ____
∞
0
____
1
1/5
1/25
1/125
1/625
1/5
b = ______
1
(0,___)
(___,0)
none
(-∞,∞)
y>0
The graph is never increasing.
(-∞,∞)
As x   , q( x) 
∞
As x   , q( x)  ____
-7/24
5
none
(-∞,∞)
y>0
x
0
____
-26/81
y>0
The graph is never increasing.
(-∞,∞)
0
As x   , r ( x)  ____
∞
As x   , r ( x)  ____
-124/375
8. How are the bases in the chart above different from the bases in problem 1?
9. What other differences do you notice?
10. Why is the graph of f ( x)  b x a horizontal line when b  1 ? Justify.
11. What do you think happens when the base equals zero?
12. Do you think an exponential function could ever have a relative maximum or a relative minimum? Explain.