November 11th
copyright2009merrydavidson
Get a graphing calculator.
Put pass in the drawer if you
are using mine.
Warm-Up
Simplify:
x2(x4) =
When multiplying a
like base you ADD the
exponents. = x6
3x4(6x-2) =
Move the x-2 to the
bottom then subtract
exponents. Only move
the x not the 6. = 18x2
(2x3)4=
When raising to a power you multiply the the
exponents of the variable but take 2 to the
fourth power. = 16x12
Exponential Functions 3.1
Definition:
y  ab
x
, where
Notice the variable is
in the exponent.
b0
“b” is the
base. “a” is
the vertical
stretch or
compression.
Determine if these are exponential
growth or decay.
1 1 x
f ( x)  (2)
3
2 is the base which is growth
but the negative x is reflect
over the y which turns
growth into decay.
f ( x)  4
x 1
2
growth
.3 is the base not the “a”
.3 is decay, Ry
x
f ( x)  .3  2 makes it growth
Graph using a graphing
calculator. Sketch the
following in your notes on the
same graph.
x
x
x
1) y  2
2) y  5
3) y  10
Label each graph.
Characteristics of Parent Exponential Functions
with b>1
1) Smooth, continuous, increasing curve
2) Domain: , 
The graphs approach y = 0

3) Range:

 0,  
but do not touch it.
y=
10x
y = 5x
y = 2x
What point do they all have in common?
(0, 1)
This is called the pivot point.
What else do you notice?


y=0
They all go thru
(1, base)
Horizontal
asymptote
The bigger the base, the
steeper the graph
Transformations on exponential
functions, are like doing
transformations on all of the other
parent functions.
Remember ALL of the rules for inside of the
function/outside of the function.
Inside of the function means
inside of the exponent.
INSIDE affects the x-coordinate
OUTSIDE affects the y-coordinate
Use this T-chart for graphing
all exponential functions.
4)
x 1
x
y
-1 0
0
1
y2
1
2
base
Where does this
graph move?
left 1
y=0
Use this T-chart for graphing
all exponential functions.
x
5)
y
0
1 3
1
3 5
base
y 3 2
x
Where does this
graph move?
Up 2
y=2
The asymptote
moves up 2
Use this T-chart for graphing
all exponential functions.
x
6)
y
0
0
1 0
-1
1
54
base
x
y  5 1
Where does this
graph move?
Ry, down 1
y = -1
You do these 3:
x 1
7)
y  3
8)
y    2  2
y=0
x
y = -2
9)
f  x  2
x 6
y=0
Write the end behavior in limit notation
for the 6 graphs you just did.
4) lim f ( x)  0; lim f ( x)  
x 
x 
5) lim f ( x)  2; lim f ( x)  
x 
x 
6) lim f ( x)  ; lim f ( x)  1
x 
x 
7) lim f ( x)  0; lim f ( x)  
x 
x 
8) lim f ( x)  ; lim f ( x)  2
x 
x 
9) lim f ( x)  0; lim f ( x)  
x 
x 
State the y-intercept and pivot point for
each of the six graphs.
Remember to find the y-intercept let x = 0.
The pivot point is what (0,1) became after
transformations.
y-intercept
pivot point
4)
(0,2)
(-1,1)
5)
(0,3)
(0,3)
6)
(0,0)
(0,0)
7)
(0,-1/3)
(1,-1)
8)
(0,-3)
(0,-3)
9)
(0,1/64)
(6,1)
TIME OUT….
“Pi” represents the irrational number that
is approximately equal to 3.14
“i” represents the imaginary number
which is the square root of -1.
“e” is the Euler Number
Approximately = 2.718
1
For every value of n: e  (1  ) n
n
You do not have to memorize this.
You only need to know that e  2.7
The Natural Base
Exponential Function
ye
x
We can do transformations
with base “e” just like any
other base.
10)
x
2
3
y
0
1
1
2.7
base
y  e
x 2
Where does this
graph move?
right 2
y=0