Download Exponential Functions and Their Graphs

1.
2.
3.
4.
5.
27 x  8
3
64 x  1
2
25 x  49
3
2
x  3x  18 x
3
2
12 x  8 x  27 x  18
3
Factoring
Practice
(5 questions)
1
Factoring Practice (Answers)
1.
2.
3.
4.
5.
(3x  2)(9 x  6 x  4)
2
(4 x  1)(16 x  4 x  1)
(5 x  7)(5 x  7)
x( x  6)( x  3)
(2 x  3)(2 x  3)(3x  2)
2
2
Exponential Functions and
Their Graphs
Sections 7-1,2,3
Objectives
• I can recognize growth or decay exponential
equations
• I can graph exponential growth and decay
parent functions
4
The exponential function f with base b is
defined by
f(x) = bx
where b > 0, b  1, and x is any real number.
For instance,
f(x) = 3x and g(x) = 0.5x
are exponential parent functions.
5
The graph of f(x) = bx, b > 1
Exponential
Growth
y
4
Range: (0, )
(0, 1)
x
4
Domain: (–, )
Horizontal Asymptote
y=0
6
The graph of f(x) = bx, 0 < b < 1
y
Exponential
Decay
4
Range: (0, )
Horizontal Asymptote
y=0
(0, 1)
x
4
Domain: (–, )
7
Example: Sketch the graph of y = 2x.
x
y
(x, y)
-2
¼
(-2, ¼)
-1
0
1
2
½
1
2
4
(-1, ½)
(0, 1)
(1, 2)
(2, 4)
y
4
2
x
–2
2
8
Definition of the Exponential Function
Put these in your calculator as y1=, y2=, y3=
And graph them simultaneously
Here are some examples of exponential functions.
f (x) = 2x
g(x) = 10x
Base is 2.
Base is 10.
h(x) = 3x
Base is 3.
9
When base is a fraction
• Graph the following on your calculator at
the same time
• y1 = (1/2)x
• y2= (3/4)x
• y3 = (7/8)x
10
Example: Sketch the graph of g(x) = 2-x. State the
domain and range.
y
The graph of this
function is a
reflection the graph
of f(x) = 2x in the yaxis.
f(x) = 2x
4
Domain: (–, )
Range: (0, )
x
–2
2
11
The graph of f(x) = ex
y
x
-2
-1
0
1
2
6
4
2
f(x)
0.14
0.38
1
2.72
7.39
x
–2
2
12
The irrational number e, where
e  2.718281828…
is used in applications involving growth and
decay.
It is a key on your calculator in the first comlum
2nd LN
13
What type is it??
• You must know if you are graphing a
growth or decay equation?
• Let’s look at some examples
14
Reflection Transformations
y  b
Rx
x
Ry
15
Reflections Change Type of
Exponential
y2
Growth
x
Decay
y2
x
y  2 Decay
x
16
Growth or Decay??
y4
x
17
Growth or Decay??
1
y 
2
x
18
Growth or Decay??
1
y  3 
 3
x
19
Growth or Decay??
1
y  3 
4
x
20
Growth or Decay??
1 x
y   3
2
21
Growth or Decay??
y  4  3
x
22
Growth or Decay??
y  2  3
x
23
Homework
• Worksheet 11-1
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