label the parts of the exponential function
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U2A L07 Log Functions as Inverses 3p Class Notes .notebook March 13, 2017
Unit 2A, FunctionsL07 Log Functions as Inverses
WALT: We are learning to: • Write and evaluate logarithmic expressions
WIMD: What I must do:• I will evaluate a logarithm• I will convert an equation from exponential form to logarithmic form
Label the parts of the Exponential Function:
n
nDomain
Range
Starting quantity
Growthfactor
Decayfactor
Number of periods
Exponent
Basey-intercept
• I will memorize and identify the parts of an exponential equation: y = abx
U2A L07 Log Functions as Inverses 3p Class Notes .notebook March 13, 2017
1 Answer?
2 Answer?
U2A L07 Log Functions as Inverses 3p Class Notes .notebook March 13, 2017
@ The MoviesPH Videos:• Evaluating logarithmic expressions• Using logarithmic expressions
3 Answer?
x = 27 y = 2
U2A L07 Log Functions as Inverses 3p Class Notes .notebook March 13, 2017
4 Answer?
y = 3 y = 1/2
U2A L07 Log Functions as Inverses 3p Class Notes .notebook March 13, 2017
5 Answer?
x = 2
Let's Review Inverse Functions
An inverse function, f-1(x), un-does what a function, f(x) does
Ex: f(x) = 2x f-1(x) = 0.5xFunction Inverse Function
f(1) = 2(1) =2 f-1(2) = 0.5(2) = 1
Ex: f(x) = x3 + 5 f-1(x) = (x-5)1/3
f(2) = 23 + 5 = 13 f-1(12) = (13-5)1/3 = 2
To derive the inverse of any function, f(x), "swap the x and y" and then re-solve for the new y.
Ex: • f(x) = bx
• y = bx
• x = by "swap x and y"• logbx = y "moved the base"• f-1(x) = logbx
U2A L07 Log Functions as Inverses 3p Class Notes .notebook March 13, 2017
So..... f(x) = by and g(x) = logbx are inverses of each other
Ex: f(x) = 2x g(x) = log2x
f(3) = 23 = 8 g(8) = log28 = 3
You can graph a function's inverse by swapping the x and y coordinates!!
y = 2x y = log2x
domain
range
asympt.
PH Videos:• Graphing a logarithmic function • using its inverse
U2A L07 Log Functions as Inverses 3p Class Notes .notebook March 13, 2017
Characteristics of Exponential FunctionsAFM Unit 2
yintercepts
xintercepts, zeros, roots
Domain and range
Rate of change and slope
Increasing and decreasing intervals
Concavity
End behavior
Minimums and maximums
Symmetry
Translations
0 2 4 6 8 10 12 14 16
1
2
3
4
1
2
3
y = log(x-2) + 3y = logx
U2A L07 Log Functions as Inverses 3p Class Notes .notebook March 13, 2017
Translating Logarithmic Functions
y = a*f(x + c) + d
Translating Functions
y = a*logb(x + c) + d
PH Videos:• Graphing a logarithmic function using a translation
U2A L07 Log Functions as Inverses 3p Class Notes .notebook March 13, 2017
Rewrite as the sum of two logs
log22x =
log612 =
Evaluate and find x using the product property
log22x = 3 x=4
log1012x = 2 x = 25/3= 81/3
do not confuse: log(M+N) ≠ log(M) + log(N)
U2A L07 Log Functions as Inverses 3p Class Notes .notebook March 13, 2017
=
6 Answer?
= 1
Rewrite as a single logarithmic expression
U2A L07 Log Functions as Inverses 3p Class Notes .notebook March 13, 2017
logbx2 logby
Rewrite as a single logarithmic expression
7 Answer?
= logb43 = logb64
= logb23 = logb8
Rewrite as a single logarithmic expression
U2A L07 Log Functions as Inverses 3p Class Notes .notebook March 13, 2017
Rewrite as a single logarithmic expression
U2A L07 Log Functions as Inverses 3p Class Notes .notebook March 13, 2017
@ The MoviesPH Videos:• Simplifying logarithms
Write each logarithmic expression as a single logarithm.
U2A L07 Log Functions as Inverses 3p Class Notes .notebook March 13, 2017
HomeworkU2A L07 HW Aleks Logs
Prentice Hall Algebra On Line ResourcesGo to "http://www.phschool.com/" then enter Web Code agk0099
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Prentice Hall Algebra On lIne Resources
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