Logarithms as Inverses

Nov 08, 2014

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Logarithms as Inverses. FoM Unit 3 Day 4. HW check. Do you recall inverses?. Investigation cont. Complete worksheet with your group. Logarithmic Functions. Ll Ll. Ll Ll.

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inverses
recall inverses
logarithmic functions
investigation cont
complete worksheet
hw check

marny-mccoy

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Logarithms as Inverses

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Logarithms as Inverses FoM Unit 3 Day 4
HW check
Do you recall inverses?

Investigation cont. • Complete worksheet with your group.
Logarithmic Functions Ll Ll Ll Ll

Logarithms

Logarithms. Geometry: Be at the back of the room, ready to go. I will be working with you first today. Algebra: Answer and turn the following problems in. Turn the following problems into radical form. 1) 5 3/4 2) 6 8/9 3) 7 2/3

447 views • 9 slides

Trig Inverses

Trig Inverses. Wikispace Final Project. y= csc (x). Opposite of y=sin(x ) To graph: 1.)First graph the function as sine. 2.) Draw asymptotes where it crosses the x-axis. 3.) Graph the opposite of sine by drawing a flipped parabola at the graphs amplitude. EXAMPLE: .

204 views • 5 slides

Investigating Inverses

Investigating Inverses. February 25, 2008. Inverse Function. T he inverse of a function reverses the x and y coordinates. In other words, for every ordered pair (x, y) in a function there will be an ordered pair (y, x) in the inverse function. .

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Logarithms

Logarithms. the inverse of exponential functions. The logarithmic functions help us work easily with very large or very small numbers….

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Logarithms

Logarithms. By: Allie, Jess, Emily, and Katie. Logarithms. This is usually written as This reads, y equals log base b of x. Textbook Definition. Logarithmic Function- The function , where b>0, and b≠1, which is the inverse of the exponential function . Algebraic Definition.

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6.4-Inverses

6.4-Inverses. Inverse: 1) Reflect over the line y=x (y-int.=0, m=1) 2.) All points have values switched ( x,y ) → ( y,x ) 3.) Equation has x & y switched, & solved for x Opposite operations exist (+ vs. - : x vs. ÷ ) 4.) Composites = x BOTH ways

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Inverses

Inverses. Inverse of a relation. Of the ordered pairs (x, y) is the set of all ordered pairs (y, x). Domain of the inverse is the range of the original. Range of the inverse is the domain of the original. Symbol: . Example: {(1,2), (2, 4), (3, 6), (4, 8)}. Inverse: .

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Inverses

Inverses. Definition. For any two matrices A and B, if AB = BA = I , then A and B are called inverse matrices The symbols A -1 denotes the inverse of matrix A If A = and det A ≠ 0 then A -1 = If det A = 0, then A has no inverse. Example 1. Find A -1 if A =

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1.4 Inverses;

1.4 Inverses; . Rules of Matrix Arithmetic. Properties of Matrix Operations. For real numbers a and b ,we always have ab=ba, which is called the commutative law for multiplication . For matrices, however, AB and BA need not be equal. Equality can fail to hold for three reasons:

1.15k views • 74 slides

Logarithms…

Logarithms…. Exponential form Change of Base Properties. Use your calculator to solve the following. 10 x = 32 x = _____ 10 x = 50 x = _____ 10 x = 207 x = _____ 10 x = 2 x = _____. Using the Log key on your calculator find each of the following. Log 32= _____

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Logarithms

Logarithms. Logarithms can be very helpful when solving exponential equations , specifically when they do not have the same base. In fact, logarithms ARE exponents. Def : What is a logarithm?

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Logarithms

Logarithms. Calculate the value of y for which 2log 3 y -log 3 ( y +4)=2. 2log 3 y -log 3 ( y +4)=2 log 3 y 2 -log 3 ( y +4)=2 log 3 ( y 2 /y +4)=2 y 2 /y +4=3 2 y 2 /y +4=9 y 2 =9( y +4) y 2 -9 y -36=0 ( y -12)( y +3)=0. Use the technique that log(x)-log(y)=log(x/y).

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Inverses

Inverses. By: Jeffrey Bivin Lake Zurich High School jeff.bivin@lz95.org. Last Updated: November 17, 2005. Definition. Inverse Relation  A relation obtained by switching the coordinates of each ordered pair. Jeff Bivin -- LZHS. INVERSE RELATIONS. x. y. { (3, 8) }. relation. Domain.

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Logarithms!

Logarithms!. Objective: To understand the history of logarithms and how to use them. Warm up. 1.) a. 4 -4 b. (x 3 ) 3 c. (-x) 9 2.) Graph y=4 x from (-3, 3). History of logs.

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1.4 Inverses;

1.4 Inverses;. Rules of Matrix Arithmetic. Properties of Matrix Operations. For real numbers a and b ,we always have ab=ba, which is called the commutative law for multiplication . For matrices, however, AB and BA need not be equal. Equality can fail to hold for three reasons:

503 views • 32 slides

7.3 Logarithmic Functions as Inverses

7.3 Logarithmic Functions as Inverses. Def: Logarithm The logarithm to the base b of a positive number y is defined: If y = b x , then log b y = x. Example: Write 729 = 3 6 and (1/2) 3 = 1/8 in log form. 729 = 3 6 can be written as log 3 729 = 6

429 views • 8 slides

Logarithms

Logarithms. Logarithms. Logarithms to various bases: red is to base e , green is to base 10 , and purple is to base 1.7 . Each tick on the axes is one unit.

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Function Inverses

Function Inverses. Lecture: 2E Pre AP & GT Precalculus. Agenda. 12 minute, 11 Question Quiz One to One Functions Inverse Functions. Injective Functions. (definition) A function for which each member of its range is associated with one and only one member of its domain.

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8.3 Logarithmic Functions as Inverses

8.3 Logarithmic Functions as Inverses. Def: Logarithm The logarithm to the base b of a positive number y is defined: If y = b x , then log b y = x. Example: Write 729 = 3 6 and (1/2) 3 = 1/8 in log form. 729 = 3 6 can be written as log 3 729 = 6

171 views • 8 slides

Logarithms

Logarithms. By: Lulu Huang, Alison Li,Gladi Pang Period 4. Product Property : log b XY = log b X + log b Y Quotient Property : log b X = log b X - log b Y Y Power property : log b X y = y logbX. 8-4 Properties of Logarithms.

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Inverses

Inverses. What do you know?. Ordered Pairs?. Domain & Range?. Equations?. Graphs are symmetric to?. f(30) =____ f -1 (8)= ______. C omposition & inverses?.

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Graphing Inverses

Graphing Inverses. Objectives. I can graph the inverse of a relation from another graph. CONCEPT OF AN INVERSE FUNCTION. Idea : An inverse switches the Input and Output of a relation to form the new inverse Note that this really says that the roles of x and y are reversed.

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