Label the parts of the Exponential Function
Transcript of Label the parts of the Exponential Function
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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