Alg1, Unit 17, Lesson01_absent-student, page 1
Graphs of exponential functions
Exponential functions have the characteristic of having the variable in
the exponent while the base is a constant:
By contrast, with power functions, the base is the variable and the
exponent is a constant.
The syntax for raising a number to a power on a graphing calculator is
to use the “^” symbol just before the exponent:
For example, 4.01 raised to the 3.7 power is written with the
following syntax on the graphing calculator:
4.01^3.7
In Examples 1 - 4, raise the indicated base to the indicated power using a graphing
calculator. Write out the syntax used on the calculator as well as the answer.
Example 1: 67.222.051
Example 2: 5.2–3.2
Example 3:
ଶ ିଷ.ଶ
ቀଷቁ
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Example 4: mp where m = 9 and p = .2
Alg1, Unit 17, Lesson01_absent-student, page 2
Example 5: Graph the exponential function y = 3x by filling in the y values in the
table, plotting each point, and then connecting the points with a smooth curve.
x
-2
-1
0
1
1.5
2
y
.111
.333
1
3
5.196
9
Asymptote:
Notice that while the curve in Example 5 approaches the x-axis, it never
actually touches the x-axis. We say that the curve asymptotically
approaches the x-axis.
In this case the asymptote is the x-axis. (An asymptote is always a line.)
Example 6: Make a sketch of f(x) = 3x + 4. (Hint: It’s the graph of Example 5 raised
4 units.)
Notice in Example 6 that the horizontal asymptote has also been raised
by 4 units. The equation of that asymptote is:
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Alg1, Unit 17, Lesson01_absent-student, page 3
Special values of the base:
If the base of an exponential function is such that 0 < b < 1 (for
example y = .5x ), then the graph looks like this.
The base of of an exponential function cannot be negative.
Example 7: Sketch the graph of y = (1/3)x – 6.
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Alg1, Unit 17, Lesson01_absent-student, page 4
Assignment:
1. Which one(s) of the following are
exponential functions?
a.
b.
c.
d.
e.
y = x3
y = 1.5x
y = 4.5(3x)4
y = x2 + 7
y = (4.2)11.12x
2. Which one(s) of the following are
power functions?
a.
b.
c.
d.
e.
y = x4 + 1
y = mx + b
y = 2(x2 + x3)
y = 4.011x + x
y=5
In problems 3-6, raise the indicated base to the indicated power using a graphing
calculator. Write out the syntax used on the calculator as well as the answer.
3. 3.5
4. 12.045–1.2
5. (1/4)–1.2
6. gh where g = 4.1 and h = -3.33
7. Which one(s) of the following
exponential functions
produce a curve that
looks like this?
8. Which one(s) of the following
exponential functions
produce a curve that
looks like this?
a.
b.
c.
d.
e.
f.
y = .6x
y = 3x - 72
y = 4x + .52
y = 11 + 5x
y = -8 + x5
y = -7 + x.4
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a.
b.
c.
d.
e.
f.
y = .6x
y = 3x - 72
y = 4x + .52
y = 11 + 5x
y = -8 + x5
y = -7 + x.4
Alg1, Unit 17, Lesson01_absent-student, page 5
9. Graph the exponential function y = (1/2)x by filling in the y values in the table,
plotting each point, and then connecting the points with a smooth curve.
x
y
-3
-2
-1
0
1
2
3
10. Make a sketch of y = (1/2)x – 8.
11. Make a sketch of y = 4x.
12. Make a sketch of y = 3x + 2 and
y = 3x – 2 on the same coordinate
system. Label the asymptotes.
13. Make a sketch of y = 3x + 2 and
y = (1/3)x + 2 on the same coordinate
system. Label the asymptotes.
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Alg1, Unit 17, Lesson01_absent-student, page 6
In problems 14 and 15, evaluate the exponential function at the given value of x
without using a calculator.
14. f(x) = (4)2x at x = 3
15. g(x) = 11(3)x at x = 2
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