Math 110
In Class Exercises, Section 4.3
Page 1 / 6
Exponential Functions: Graphing
Goal: Be able to graph exponential functions, both using your calculator, and by hand
1) Graph the following exponential function by hand, then check your work using a calculator:
x
y2
Make sure that you clearly label where the points are. For each point, show all your work!
 (-1, f(-1) )
 (0, f(0) )
 (1, f(1) )
 Clearly indicate where the horizontal asymptote is
 What is the domain of the function?
X
 What is the range?
10
9
8
7
6
5
4
3
2
1
0
-1
-1 -9 -8 -7 -6 -5 -4 -3 -2 -1 0
-2
0
-3
-4
-5
-6
-7
-8
-9
-10
1
2
3
4
5
6
7
8
9 10
Y
Math 110
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Math 110
In Class Exercises, Section 4.3
Page 2 / 6
2) Graph the following exponential function by hand, then check your work using a calculator:
x
1
y 
2
Make sure that you clearly label where the points are. For each point, show all your work!
 (-1, f(-1) )
 (0, f(0) )
 (1, f(1) )

 Clearly indicate where the horizontal asymptote is
 What is the domain of the function?
X
 What is the range?
10
9
8
7
6
5
4
3
2
1
0
-1
-1 -9 -8 -7 -6 -5 -4 -3 -2 -1 0
-2
0
-3
-4
-5
-6
-7
-8
-9
-10
1
2
3
4
5
6
7
8
9 10
Y
Math 110
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Math 110
In Class Exercises, Section 4.3
Page 3 / 6
Exponential Functions: Graphing
Goal: Be able to graph exponential functions, both using your calculator, and by hand
3) Graph the following exponential functions on the same graph, using a calculator:
x
y2
y  2x
4) Graph the following exponential functions on the same graph, using a calculator:
x
y  10
y 10 x
5) Graph the following exponential functions on the same graph, using a calculator:
x
y7
y  7 x
6) Given what you’ve seen in the previous three questions, what effect does a negative sign have,
when it’s applied directly to x? Can you explain why this happens?
7) Graph the following exponential functions on the same graph, using a calculator:
x
y2
y  2 x
8) Graph the following exponential functions on the same graph, using a calculator:
x
y  10
y  10 x
9) Given what you’ve seen in the previous three questions, what effect does a negative sign have,
when it’s applied directly to x? Can you explain why this happens?
Math 110
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Math 110
In Class Exercises, Section 4.3
Page 4 / 6
10) Graph the following exponential function by hand, then check your work using a calculator:
Make sure that you clearly label where the points (-1, f(-1)), (0, f(0)), and (1, f(1)) have been
transformed to. (I.e., on the original graph of 2x, (0,f(0)) ends up being at (0,1). On the transformed function below,
X
that point has been moved to (-1, 0) – it was moved left one, and down one. )
10
9
8
7
6
5
4
3
2
1
0
-1 0 1
-1 -9 -8 -7 -6 -5 -4 -3 -2 -1
-2
0
-3
-4
-5
-6
-7
-8
-9
-10
y  2 x 1  1
What is the domain? Range?
Where is the horizontal
asymptote?
2 3 4 5 6 7 8 9 10
Y
X
11) Graph the following exponential function by hand, then check your work using a calculator:
Make sure that you clearly label where the points (-1, f(-1)), (0, f(0)), and (1, f(1)) have been
transformed to.
 x 1
10
9
8
7
6
5
4
3
2
1
0
-1
-1 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1
-2
0
-3
-4
-5
-6
-7
-8
-9
-10
y2
1
What is the domain? Range?
Where is the horizontal
asymptote?
2 3 4 5 6 7 8 9 10
Y
Math 110
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Math 110
In Class Exercises, Section 4.3
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X
12) Graph the following exponential function by hand, then check your work using a calculator:
Make sure that you clearly label where the points (-1, f(-1)), (0, f(0)), and (1, f(1)) have been
transformed to.
x 1
10
9
8
7
6
5
4
3
2
1
0
-1
-1 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1
-2
0
-3
-4
-5
-6
-7
-8
-9
-10
1
y
2
1
What is the domain? Range?
Where is the horizontal
asymptote?
2 3 4 5 6 7 8 9 10
Y
X
13) Graph the following exponential function by hand, then check your work using a calculator:
Make sure that you clearly label where the points (-1, f(-1)), (0, f(0)), and (1, f(1)) have been
transformed to.
x
10
9
8
7
6
5
4
3
2
1
0
-1
-1 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1
-2
0
-3
-4
-5
-6
-7
-8
-9
-10
 
y  1 3 2
What is the domain? Range?
Where is the horizontal
asymptote?
2 3 4 5 6 7 8 9 10
Y
Math 110
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Math 110
In Class Exercises, Section 4.3
Page 6 / 6
Exponential Functions: Solving them
14) Solve the following equation for x:
x 1
3
 81
15) Solve the following equation for x:
3 x 1
 100
10
16) Solve the following equation for x:
4 x 
1
1024
17) Solve the following equation for x:
4 x
x2
12
e 
e
e
18) Solve the following equation for x:
1 x
1
 
2
4
Math 110
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