APC
Unit 4
Logarithmic Functions
Warm-up
What
is the domain and range of an
exponential function
A) f(x) = 3x
B) g(x) = 2e(x-2)+3
The
domain of a function is equal to the
__________ of its inverse function
The range of a function is equal to the
___________ of its inverse function
Review Homework
#54
(x) (-x) reflect over y-axis
(-3) reflect over the x-axis and vertically
stretch x3
(+9) Shift up 9 units
Key learnings
Exponential
functions
Look for transformations that shift the graph
up or down
Moves the horizontal asymptote
Move the key point
Starts
at (0,1)
#92
Break
into 2 problems
X<0
X>0
is reflected over the y-axis
The
power of a sketch
Activity – You Try it…
text
Relating exponential and log
functions
Key Skill
Changing from Log form to equivalent
exponential form
The base of the log becomes the base of the
exponent
Remember this one to get the pattern
This is an equivalent equation
This is not the inverse
Evaluating Logrithms
Set
the log equal to x
Re-write
in exponential form
Evaluate
the value of x that
makes the equation true
Try Worksheet #2, 3, and 4
Calculator
LOG
LN
– log base 10
– Natural Log – Log base “e”
Try with and without your
Calculator
Transforming Log Functions
Look
for transformation that shifts left/right
Moves the vertical asymptote
Move
the key point
Starts at (1,0)
Practice
Solving Logrithmic Equations
Try
writing the equivalent exponential
equation
To get the variable out of the log( )
Solve
for x
Check your answers
No log of Negative numbers
Solving Logrithmic Equations
Problems from the homework
To
evaluate log expressions
Remember to add = x
Write as an exponent
Then evaluate
0
