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Block 3
Exponential and Logarithmic
Graphs
What is to be learned?
• What an exponential function is
• How to draw an exponential function
graph
• How to identify exponential functions.
Basic exponential Functions
Are in form y = ax
Remember a0
= 1
y = 3x
x 0 1 2 3 4 5
yy 1 3 9 27 81 243
y = 3x
x 0 1 2 3 4 5
y 1 3 9 27 81 243
y = 3x
y = 4x
y = 2x
(0 , 1)
Identifying Exponential Graphs
y = ax
1
(2 , )64
value of a?
x y
x = 2, y = 64
substituting
64 = a2
a = 8
find a
equation
y = 8x
y = 3x
y = 4x
y = 2x
(0 , 1)
Exponential Functions
• Exponentials are in form y = ax
Identifying Exponential Graphs
y = ax
1
(2 , )36
value of a?
x y
x = 2, y = 36
substituting
36 = a2
a = 6
find a
equation
y = 6x
You Try
1
(2 , 81)
All of these graphs are in the form y = ax
Find the equations
1
(3 , 8)
1
(3 , 125)
1
(4 , 81)
Key Question
1. 2.
3. 4.
y = 9x
y = 2x
y = 5x y = 3x
What is to be learned?
• What a logarithmic function is
• How to draw a logarithmic function graph
Logarithmic Functions
The inverse of exponential functions.
( Reflection in line y = x )
The inverse of y = 5x
is written
y = log5x
Sketching Log Graphs
y = 3x
y = x
y = log3x
1
(2 , )9
1
(9 , 2)
y = log3x Sketch Inverse First
Logarithmic Functions
The inverse of exponential functions.
( Reflection in line y = x )
The inverse of y = 5x
is written
y = log5x
Ex Sketch y = log4x
y = 4x
y = x
y = log4x
1
(2 , )16
1
(16 , 2)
Sketch Inverse First
Sketch y = log5x + 2
y = 5x
y = x
y = log5x
1
(2 , )25
1
(25 , 2)
Key Question
(1 , 2)
(25 , 4)
Show two points on graph