Date post: | 18-Jan-2018 |
Category: |
Documents |
Upload: | theodore-howard |
View: | 223 times |
Download: | 0 times |
Exponential Functions and Their Graphs
2
Exponential Function Families
• We’ve already learned about – This is the parent function
• We’ll expand this to – Note a=1 and h=0 in the parent function
xaby
kaby hx )(
3
Component Property
+ k Vertical shift up- k Vertical shift down- h Horizontal shift to the right+ h Horizontal shift to the left
a > 1 Stretcha < 1 Compression
-a Reflection
kaby hx )(
4
The graph of f(x) = ax, a > 1y
x(0, 1)
Domain: (–, )
Range: (0, )
Horizontal Asymptote y = 0
4
4
5
The graph of f(x) = ax, 0 < a < 1y
x(0, 1)
Domain: (–, )
Range: (0, )Horizontal Asymptote
y = 0
4
4
6
Example: Sketch the graph of f(x) = 2x.
x
x f(x) (x, f(x))-2 ¼ (-2, ¼)-1 ½ (-1, ½)0 1 (0, 1)1 2 (1, 2)2 4 (2, 4)
y
2–2
2
4
7
Example: Sketch the graph of g(x) = 2x – 1. State the domain and range.
x
yThe graph of this function is a vertical translation of the graph of f(x) = 2x
down one unit .
f(x) = 2x
y = –1 Domain: (–, )
Range: (–1, )
2
4
8
Example: Sketch the graph of g(x) = 2-x. State the domain and range.
x
yThe graph of this function is a reflection the graph of f(x) = 2x in the y-axis.
f(x) = 2x
Domain: (–, )
Range: (0, ) 2–2
4
9
The graph of f(x) = ex
y
x2 –2
2
4
6
x f(x)-2 0.14-1 0.380 11 2.722 7.39
10
The irrational number e, where
e 2.718281828…
is used in applications involving growth and decay.
11
Pert
12
Continuously Compounded Interest
rtePtA )(
13
Pert ExampleSuppose you won a contest at the start of 5th grade that deposited $3000 in an account that pays 5% annual interest compounded continuously. How much will you have in the account when you enter high school 4 years later? Express the answer to the nearest dollar.
rtePtA )()4)(05(.3000)4( eA
2.3000)4( eA 3664$)4( A