BOB

hi, this is Ale
Today is a test and i hope every one of us is preparing himself for the morning test. a lot have been reminded by our dear classmate but i also want to remind you two thing adding on what our friend have already said.

1. don't forget to write your answers in 4 decimal places
   
2. when using a calculator in order to be accurate remember to store your answers in Alpha A
   

Good luck everyone and lets hope the test will be done in a good condition and everyone will finish it smiling

Relationship between exponent and logarithm

Hi, this is Ale, I am sorry for the delay in posting. On Friday we learned the relationship between an exponent and logarithm. In order to understand how logarithm work we need to remember exponential function because a logarithm is a inverse of an exponential function.
What a function does its inverse undoes it. We also have to remember that the exponential function is of form

Where b is the base a is the exponent or the input in case of a function and x is the power.The most important thing we learned is that the logarithm is an exponent. With The famous formula

the exponential function turns the input into power so its inverse which is a logarithm will turn the power exponent

for example if 4² = 16, exponent then its inverse will be log₄16 = 2

We also have to know that every exponent function has a base of 1

W

http://www.themathpage.com/aPreCalc/logarithmic-exponential-functions.htm

exponential function has x as asymptote but its inverse which logarithm has y as asymptote

We also learned logarithmic laws or rules. As logarithm is an exponent. many law applied to exponent are also used for logarithm

Product law

for exponent :(a^b) ^x = a^b*x

eg:(2²)² = 2^2*2 = 2⁴

• log _b MN = log _b M*log _b

Eg: log ₂(8*16) = log ₂ 8*log ₂ 16

3 + 4 = 7

• log _b (M/N) = log _b M-log _b N

Eg: log ₂(32/138) = log ₂ 32*log ₂ 13

5 - 7 = -2

The power law

• log _bM ^k = klog _bM

eg : log ₂8⁵ = 5log ₂8

Special cases

If the base and the power are the same the result is the same

• log _bx^y= y

if a base is rased to a power and log is the same base the power

• log ^{logb x} = x

http://www.mathwords.com/l/logarithm_rules.htm
http://www.sosmath.com/algebra/logs/log4/log44/log44.html
http://www.purplemath.com/modules/logrules.htm
http://www.youtube.com/watch?v=PupNgv49_WY

the next scribe is Kale

graphing reciprocal functions

Hi, this is ALE in today class we learned how to graph reciprocal function. We first started with some workshop exercise. we were asked to sketch

( the solution to these two exercise are on Mr K slides of March 5, 2009)

the most important thing is to remember that a multiplicative inverse of an number also called reciprocal is defined by the formula one over that number.

In other word the reciprocal function p can be defined by the rule

p(x)= 1/x

For example if given: 1; 2; 3; 25 ; 45; 999999n their reciprocal will be

1/1 for 1 1/2 for 2, 1/3 for 3 1/25 for 25 1/45 for 45 and 1/999999 for 999999

we also have to remember when dealing with inverses that as the number of the first raw are bigering the number on the second raw are smollaring in our example we have the case of 1, 2, 3 are begering and the number 1/1=1 , 1/2= 0.5 and 1/3= 0.33333 smollaring

After talking about the reciprocal function we also learned about how to graph them. there are different steps

• draw the original graph of the function before transformation
• then diffine the invariant points (Point that don't move or change after the transformation into reciprocal function)
• determine the roots of the function or the vertical assymptote (values that makes the denominator equal to zero)
• After defining the assymptote, manupulate the game of biggering and smallering

for more information about reciprocal function follow the link bellow

• http://http//en.wikipedia.org/wiki/Reciprocal_(mathematics)
• http://http//www.coolschool.ca/lor/PMA11/unit3/U03L05.htm
• http://http//www.themathpage.com/aPrecalc/rational-functions.htm
• http://http//www.purplemath.com/modules/invrsfcn3.htm

This is what we learned in class, The next scribe is honorable Aldrin