Exponential Functions: Graphing, Solving Equations, and Population Growth, Study notes of Algebra

Various problems on exponential functions, covering topics such as graphing, determining domain, range, and horizontal asymptote, and solving equations. The document also includes a problem on population growth.

Typology: Study notes

2011/2012

Uploaded on 12/31/2012

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Lesson
Exponential Functions
Use transformations to
g
raph the function. Determine the domain, ran
g
e, and horizontal as
y
mptote of
the function.
1) f(x) = -2x+3 + 4
x
-10 -5 5 10
y
10
5
-5
-10
x
-10 -5 5 10
y
10
5
-5
-10
Graph the function.
2) f(x) = 2- x - 3
x
-5 -4 -3 -2 -1 1 2 3 4 5
y
5
4
3
2
1
-1
-2
-3
-4
-5
x
-5 -4 -3 -2 -1 1 2 3 4 5
y
5
4
3
2
1
-1
-2
-3
-4
-5
CollegeAlgebra
pf3
pf4

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Lesson

Exponential Functions

Use transformations to graph the function. Determine the domain, range, and horizontal asymptote of

the function.

1) f(x) = -2x+3 + 4

-10 -5 5 10 x

y 10

-10 -5 5 10 x

y 10

Graph the function.

2) f(x) = 2- x - 3

-5 -4 -3 -2 -1 1 2 3 4 5 x

y 5 4 3 2 1

-5 -4 -3 -2 -1 1 2 3 4 5 x

y 5 4 3 2 1

3) f(x) = ex - 5

-6 -4 -2 2 4 6 x

y 6 4

2

-6 -4 -2 2 4 6 x

y 6 4

2

Solve the equation.

4) 2 1 + 2x = 8

5) 14x = 1

6) 3 -x =

7) 4 5 - 3x =

8) 4x = 16

9) 3 (3x - 6 ) = 27

10) 2 x2 - 3= 64

11) 92x · 27(3 - x) =

12) (ex)x · e^24 = e10x

13) ex - 3 =

e^6

x + 5

Answer Key

Testname: 19_EXPONENTIAL_FCT

-10 -5 5 10 x

y 10

-10 -5 5 10 x

y 10

domain of f: (-∞, ∞); range of f: (-∞, 4);

horizontal asymptote: y = 4

-5 -4 -3 -2 -1 1 2 3 4 5 x

y 5 4 3 2 1

-5 -4 -3 -2 -1 1 2 3 4 5 x

y 5 4 3 2 1

-6 -4 -2 2 4 6 x

y 6 4 2

-6 -4 -2 2 4 6 x

y 6 4 2