Notes 7.1 Graphing Exponential Functions(in progress).notebook
January 29, 2015
Notes 7.1 - Graphing Exponential Functions
You can graph repeated multiplication with function of the form y = abx. We call this an exponential function as long as and
.
Graph: y = 2
x
x
y
Notes 7.1 Graphing Exponential Functions(in progress).notebook
Now, let's talk important features!
All exponential graphs (without any shifting) have the following important features to consider:
Reference Point: (0, 1)
Asymptote: y = 0
.
Horizontal dotted line
drawn AFTER shifting!
January 29, 2015
Notes 7.1 Graphing Exponential Functions(in progress).notebook
January 29, 2015
Writing Activity!
What is the purpose of an asymptote? Why would an exponential function have an asymptote at y = 0?
Sample Answer: An asymptote is a boundary line that shows where a graph cannot exist. An exponential function has an asymptote at y = 0 because regardless of the type of exponent, the result will never be negative. So, the y = 0 asymptote shows that the result/output of the graph will always be greater than zero.
Notes 7.1 Graphing Exponential Functions(in progress).notebook
Now, let's talk shifting!
y = ab(x­h) + k
a = initial amount
b = base
h = opposite horizontal shift
k = regular vertical shift
You must adjust your asymptote and reference point accordingly!
January 29, 2015
Notes 7.1 Graphing Exponential Functions(in progress).notebook
January 29, 2015
Graph and identify all important features.
2. f(x) = 3x + 2
1. f(x) = 3x+1
End Behavior:
Ref Point:
Ref Point:
Asymptote:
Asymptote:
Domain:
Domain:
Range:
Range:
End Behavior:
Notes 7.1 Graphing Exponential Functions(in progress).notebook
January 29, 2015
Graph and identify all important features.
4. f(x) = 2x+5 ­ 6
3. f(x) = 2x­3 ­ 1
End Behavior:
Ref Point:
Ref Point:
Asymptote:
Asymptote:
Domain:
Domain:
Range:
Range:
End Behavior:
Notes 7.1 Graphing Exponential Functions(in progress).notebook
January 29, 2015
Graph and identify all important features.
5. End Behavior:
6. Ref Point:
Ref Point:
Asymptote:
Asymptote:
Domain:
Domain:
Range:
Range:
End Behavior:
Notes 7.1 Graphing Exponential Functions(in progress).notebook
January 29, 2015
Graph and identify all important features.
7. End Behavior:
8. Ref Point:
Ref Point:
Asymptote:
Asymptote:
Domain:
Domain:
Range:
Range:
End Behavior:
Notes 7.1 Graphing Exponential Functions(in progress).notebook
January 29, 2015
What about this craziness????
HINT
9. Ref Point:
Asymptote:
Domain:
Range:
End Behavior:
: Thin
k of th
e - as
a coeff
icient (
a) of 1!
Notes 7.1 Graphing Exponential Functions(in progress).notebook
January 29, 2015
Application!
Exponential Growth and Decay
A(t) = a(1 + r)t
Time
Ending Amount
Time
Initial
Amount
Rate of growth
or decay
10. You invested $1000 in a savings account at the end of 6th grade. The account pays 3% interest annually. How much money will be in the account after 6 years?
Notes 7.1 Graphing Exponential Functions(in progress).notebook
January 29, 2015
ADD Reference Point, Asymptote, Domain and Range to #13 ­ 21!