Lesson+Summaries

Wednesday November 16, 2010 Edited by: Mariam
 * Day 1 - Reviewing Exponential Functions**

Form of the Function: **f(x) = b ﻿^ x** b- base x - exponent (variable)

__What are the finite differences of y = 2^x__ Therefore, can conclude that the finite differences of the exponential functions are exponential as well, and copy the actual functions values.
 * ~  ||~ f(x) = 2^x ||~ f(x) = (1/2)^x ||
 * Domain || {x| xER} || {x|xER} ||
 * Range || {y|y>0, yER} || {y|y>0, yER} ||
 * y-intercept || 1 || 1 ||
 * any asymptotes? where? || y = 0 || y= 0 ||
 * x || y || ∆y1 || ∆y2 || ∆y3 || ∆ Y4 ||
 * 0 || 1 || 1 || 1 || 1 || 1 ||
 * 1 || 2 || 2 || 2 || 2 || 2 ||
 * 2 || 4 || 4 || 4 || 4 || 4 ||
 * 3 || 8 || 8 || 8 || 8 || 8 ||
 * 4 || 16 || 16 || 16 || 16 ||  ||
 * 5 || 32 || 32 || 32 ||  ||   ||
 * 6 || 64 || 64 ||  ||   ||   ||
 * 7 || 128 ||  ||   ||   ||   ||

__Working with Exponential Expressions and Equations__ - Examples

2^x = 2^2 x = 2 || 2. 2^x = 16 2^x = 2^4 x= 4 || 4^ (x+5) = 4^(3x) x+5 = 3x 5 = 2x 5/2 =x || 4. 4^ (2x) = 8^ (x-3) 2^ (4x) = [2^3]^(x-3) 2^ (4x) = 2^(3x – 9) 4x = 3x-9 x= -9 || __Homework:__ Exponential Expression and Equations multiple choice hand out
 * 1. 1. 2^x = 4
 * 3. 4^ (x+5) = 64^x

__For more information visit:__ __[|Grade 11 Exponential Functions Review]__ __[|Exponent Laws]__ (check out if you had difficulty with the homework)

**By: Gwynne Finlay**
Sorry, I don't know how to make the font subscript. So, I just wrote subscript after the number. Mostly the numbers are after the log so just to let you know that means it has to be "the little writing".

__b --> base__
x=b^y logbx=y (said "log base b of x is equal to y")

**eg. express as a logarithm** a) 2^4=16 --> log2(subscript)16=4

b) a^c=d --> loga(subscript)d=c

**eg. express as an exponent** a)log5(subscript)125=3 --> ^3=125

b) loge(subscript)f=k -->e^k=f

**eg. solve** a) log3(subscript)81 3^x=81  3^x=3^4  x=4

__**Common Logarithm**__
--> the log button on your calculator is to the base of 10 --> log10(subscript) you can only use the log button on your calculator if the subscript after is a 10 **eg.** a) log10(subscript)100 x=2

b) log 10000 **<-- when nothing is placed after the log it means that there is an invisible 10 there.** x=4

c) log120 x=2.08

**Homework: -- to finish the "Home Activity" worksheet** **Wise Words from Gillian -- make sure to understand exponential functions so that you can understand logarithms!** **-- make sure to do the previous sheet (solving exponential functions) and understand it because you use them often!**

__**Monday November 22 2010**__ Brittney West I have posted this morning's lesson below. Gillian gave us a homework sheet today in class. Also, we are to derive the quotient rule. (see lesson) Remember to check your email tonight about tomorrows field trip!

If you're struggling with this topic, here's a helpful link: []

=Path System= Tuesday, November 23 Mimi Chen

Today we had a field trip to downtown Toronto where we did math in public places! We learned that math can be found anywhere, and that people stare when you walk with a calculator in hand.

Brittney West Tomorrow we have a quiz!! Below I have posted an attachment to a //brief// summary as well as today's lesson. Gillian handed out our "Bonus Assignment" today which is due on Friday!
 * __Monday November 29 2010__**

If you're struggling with any of these topics, the website below is very helpful! :) []

Topic: **Applications of Logarithms** Tuesday November 30th, 2010 Edited by: Mariam Naguib

Today we had a LOG quiz, a Teamwork Tuesday (handed in, in class) and a short lesson (attatched below) Homework: Applications Hand Out + Textbook pg. 131 # 1-12, pg. 134 # 1-19, pg. 148 #2, 6, 10, 11. For more info: [|Richter Scale and pH Scale] [|Sample Word Problems]

Edited by Robert Piggott
 * Wednesday, December 1, 2010**

MATH AT MAC - math contest today!!!!

Edited by: Aleena Dipede
 * Friday, December 3rd, 2010 - __Transforming Log Functions__ **

To begin, we got in partners and discussed the following questions and these are some of the idea we came up with.

Question 1: A negative integer is the logarithm (base 10) of the number A. What do you know about number A? - it's an exponent of 10 - 0 < a < 1 - A is always postive

Question 2: A number in the form _.5 where _ is a whole number, is a logarithm (base 10) of the number A. What do you know about A? - A ≥ √4 - log4A = _.5 - 4_.5= A

Here is a summary of the activity we did on the GIZMO. If you would like to access the GIZMO the login is **TORONDSB1269** and the pass is **science**.

Here's the gist...

The standard form of the logarithm is y = logb(x) Where b and x are both positive integers and b ≠1

<span style="font-family: Arial,Helvetica,sans-serif;">The x-intercept of the standard function is always 1 <span style="font-family: Arial,Helvetica,sans-serif;">The asymptote of the standard function is x=0, so the graph can never touch the y-axis.

<span style="font-family: Arial,Helvetica,sans-serif;">Image from: [] <span style="font-family: Arial,Helvetica,sans-serif;">When a > 1 the graph curves up and when 0 < a < 1 the graph curves downwards.

<span style="font-family: Arial,Helvetica,sans-serif;">Now when we transform the function it takes this form

<span style="font-family: Arial,Helvetica,sans-serif;">Y = a logb [c(x-h) + k]

<span style="font-family: Arial,Helvetica,sans-serif;">"h" is a phase shift and moves the asymptote and changes the restrictions in the domain. <span style="font-family: Arial,Helvetica,sans-serif;">Example. Horizontal Shifts <span style="font-family: Arial,Helvetica,sans-serif;">

<span style="font-family: Arial,Helvetica,sans-serif;">Image from: []

<span style="font-family: Arial,Helvetica,sans-serif;">"k" is a verticle translation <span style="font-family: Arial,Helvetica,sans-serif;">Example. Vertical Shifts <span style="font-family: Arial,Helvetica,sans-serif;">

<span style="font-family: Arial,Helvetica,sans-serif;">Image from: [] <span style="font-family: Arial,Helvetica,sans-serif;">"a" is a verticle stretch or compression and if (-ve) a reflection in the x-axis

<span style="font-family: Arial,Helvetica,sans-serif;">"c" is a horizontal stretch or compression

<span style="font-family: Arial,Helvetica,sans-serif;">Our homework is to start studying by finishing up any homework that has not been completed yet (including the lesson on the GIZMO and the review package we recieved)

<span style="font-family: Arial,Helvetica,sans-serif;">If you want more information this link has three pages on transforming logs and goes through examples, pretty helpful... []

__**Tuesday December 7 2010**__ By: Sarah Drury Today we wrote our Exp/Trig unit test.

December 10 Gwynne Finlay Today we worked on the computer.