5.3 Logarithmic Functions

Comic of the Day

Practice: What function could describe the graph above?

Warm Up
Try simplifying the following expressions to see if they would be helpful steps to solve the exponential equation   

a) 

b)     

c) 


Announcements

• Next quiz tentatively scheduled for Mon, Feb 4 (4.5 Rational Functions, 5.1-5.3 Exponential and Logarithmic Functions)
• Next unit exam Wed, Feb 13 (55 minutes, in class)

Today - 5.3 Logarithmic Functions
My x is trapped in a castle! How will I get her down? I need a hero!
http://youtu.be/puTtnqoqHLQ

Notes
Graph of 

Homework
5.3 #9-67

Tomorrow - 5.3 Logarithmic Functions continued
Pre-read 5.3
Add 5.3 #69-101 odd to homework

For more information
https://www.khanacademy.org/math/algebra/logarithms-tutorial/logarithm_basics/v/logarithms
https://www.khanacademy.org/math/algebra/logarithms-tutorial/logarithm_basics/v/logarithmic-equations-2
https://www.khanacademy.org/math/algebra/logarithms-tutorial/logarithm_basics/e/logarithms_1
https://www.khanacademy.org/math/algebra/logarithms-tutorial/logarithm_basics/v/fancier-logarithm-expressions
https://www.khanacademy.org/math/algebra/logarithms-tutorial/logarithm_basics/e/logarithms_1.5
https://www.khanacademy.org/math/algebra/logarithms-tutorial/logarithm_basics/v/graphing-logarithmic-functions

5.2 Exponential Functions

Comic of the Day

Tip: Order of OPerationS is the OoPS you don't want to make.  Also, mnemonics like SOH CAH TOA are great study aids.

Warm Up
Simplify the following using exponent laws.  Express your answer using positive exponents only.









Announcements

• Next quiz tentatively scheduled for Mon, Feb 4 (4.5 Rational Functions, 5.1-5.3 Exponential and Logarithmic Functions)
• Next unit exam Wed, Feb 13 (55 minutes, in class)

Today - 5.2 Exponential Functions
Attack of the Frankexponent Monster!
http://youtu.be/8H3dFh6GA-A
Graph of

Notes

Homework
5.2 #1-45, 51-75 odd

Tomorrow - 5.3 Logarithmic Functions
Pre-read 5.3

For more information
https://www.khanacademy.org/math/trigonometry/exponential_and_logarithmic_func/exp_growth_decay/v/exponential-growth-functions
https://www.khanacademy.org/math/trigonometry/exponential_and_logarithmic_func/exp_growth_decay/v/graphing-exponential-functions
https://www.khanacademy.org/math/trigonometry/exponential_and_logarithmic_func/continuous_compounding/v/introduction-to-compound-interest-and-e

5.1 Inverse Functions

Comic of the Day

Warm Up
Find the asymptotes and intercepts of the function, then graph;


Announcements

• Next quiz tentatively scheduled for Mon, Feb 4 (4.5 Rational Functions, 5.1-5.3 Exponential and Logarithmic Functions)
• Next unit exam Wed, Feb 13 (55 minutes, in class)

Today - 5.1 One-to-One and Inverse Functions
Notes

Homework
5.1 #1-87 odd

Tomorrow - 5.2 Exponential Functions
Pre-read 5.2

For more information

http://patrickjmt.com/inverse-functions-the-basics/
http://patrickjmt.com/finding-the-inverse-of-a-function/
http://patrickjmt.com/finding-the-inverse-of-a-function-or-showing-one-does-not-exist-ex-2/
http://patrickjmt.com/finding-the-inverse-of-a-function-or-showing-one-does-not-exist-ex-3/
http://patrickjmt.com/finding-the-inverse-of-a-function-or-showing-one-does-not-exist-ex-4/

https://www.khanacademy.org/math/algebra/algebra-functions/function_inverses/v/introduction-to-function-inverses
https://www.khanacademy.org/math/algebra/algebra-functions/function_inverses/v/function-inverse-example-1
https://www.khanacademy.org/math/algebra/algebra-functions/function_inverses/v/function-inverses-example-2
https://www.khanacademy.org/math/algebra/algebra-functions/function_inverses/v/function-inverses-example-3
https://www.khanacademy.org/math/algebra/algebra-functions/function_inverses/e/inverses_of_functions

4.5 Rational Functions

Comic of the Day

Tip: It's okay to laugh at math jokes in math class.  You're among your nerd friends now.

Warm Up
a) Graph using intercepts

b) Graph using transformations


Announcements

• Next quiz tentatively scheduled for Mon, Feb 4 (4.5 Rational Functions, 5.1-5.3 Exponential and Logarithmic Functions)
• Next unit exam Wed, Feb 13 (55 minutes, in class)

Today - 4.5 Rational Functions
Notes

Homework
4.5 #1-77 odd

Tomorrow - 5.1 One-to-One and Inverse Functions
Pre-read 5.1

For more information
https://www.khanacademy.org/math/algebra/rational-expressions/rational-function-graphing/v/asymptotes-of-rational-functions
https://www.khanacademy.org/math/trigonometry/polynomial_and_rational/asymptotes-graphing-rational/v/another-rational-function-graph-example
https://www.khanacademy.org/math/trigonometry/polynomial_and_rational/asymptotes-graphing-rational/v/a-third-example-of-graphing-a-rational-function
http://patrickjmt.com/graphing-some-basic-rational-functions-example-1/
http://patrickjmt.com/graphing-a-rational-function-example-1/
http://patrickjmt.com/graphing-a-rational-function-example-2/
http://patrickjmt.com/graphing-a-rational-function-example-3/
http://patrickjmt.com/graphing-a-rational-function-example-4/
http://patrickjmt.com/shortcut-to-find-horizontal-asymptotes-of-rational-functions/
http://patrickjmt.com/finding-vertical-asymptotes-of-rational-functions/
http://patrickjmt.com/finding-slant-asymptotes-of-rational-functions/
http://patrickjmt.com/find-asymptotes-of-a-rational-function-vertical-and-obliqueslant/
http://patrickjmt.com/find-asymptotes-of-a-rational-function-vertical-and-obliqueslant-ex-2/
http://patrickjmt.com/graphing-a-rational-function-that-has-an-obliqueslant-asymptote-and-a-vertical-asymptote/

10.2 Completing the Square with Circles

Comic of the Day

Tip: Show your work.  If you entered something into your calculator (or Google...), then write what you entered in your calculator (or Google...)

Warm Up
Find the zeros of the function 

Hint: Rewrite as


Announcements

• Next quiz scheduled for Thu, Jan 24 (4.3 Advanced Factoring, 10.2 Completing the Square with Circles)
• Next unit exam Fri, Jan 25 (55 minutes, in class)

Today - 10.2 Completing the Square with Circles
Kuta Software Worksheet on Circles (link to solutions plus other worksheets available on Moodle)

Homework
10.2 #1-17 odd

Tomorrow - Review
You bring questions, I bring answers.

Unit Test Friday
I bring questions, you bring answers

For more information
http://patrickjmt.com/the-center-radius-form-for-a-circle-a-few-basic-questions-example-1/
http://patrickjmt.com/finding-the-center-radius-form-of-a-circle-by-completing-the-square-example-1/

4.3 Graphing Polynomials - Advanced

Comic of the Day

Tip: Label the critical points on your graphs.

Warm Up
Find the all the zeros of the function 



Announcements

• Next quiz scheduled for Thu, Jan 24 (4.3 Advanced Factoring, 10.2 Completing the Square with Circles)
• Next unit exam Fri, Jan 25 (55 minutes, in class)

Today - 4.3 Graphing Polynomials - Advanced
Notes 

Homework
4.3 #49-53 odd

Tomorrow - 10.2 Completing the Square with Circles

For more information
http://patrickjmt.com/finding-all-the-zeros-of-a-polynomial-example-1/
http://patrickjmt.com/finding-all-the-zeros-of-a-polynomial-example-2/
http://patrickjmt.com/finding-all-the-zeros-of-a-polynomial-example-3/
http://patrickjmt.com/finding-the-formula-for-a-polynomial-given-zerosroots-degree-and-one-point-example-1/
http://patrickjmt.com/finding-the-formula-for-a-polynomial-given-zerosroots-degree-and-one-point-example-2/
http://patrickjmt.com/finding-the-formula-for-a-polynomial-given-zerosroots-degree-and-one-point-example-3/
http://patrickjmt.com/rational-roots-test/

4.3 Factor and Remainder Theorem

Comic of the Day

Tip: Try to make your studying an active process, by creating diagrams, flow charts, flash cards, etc.

Warm Up
Use synthetic division to determine whether x-1 is a factor of x³+4x²-x-3


Announcements

• Next quiz tentatively scheduled for Thu, Jan 24 (4.3 Advanced Factoring, 10.2 Completing the Square with Circles)
• Next unit exam Fri, Jan 25 (55 minutes, in class)

Today - 4.3 Remainder and Factor Theorems
Notes 

Homework
4.3 #23-47, 65 odd (skip #35)

Tomorrow - 4.3 Graphing Polynomials - Advanced

For more information
http://patrickjmt.com/the-remainder-theorem-example-1/
http://patrickjmt.com/the-remainder-theorem-example-2/

4.3 Synthetic Division

Comic of the Day

Tip: Check your answer after each question while doing your homework.  No sense doing them all the wrong way.

Warm Up
a) Use long division to determine whether x+1 is a factor of x³+4x²-x-3
b) Divide 1403÷12 by long division

Announcements

• Next quiz tentatively scheduled for Thu, Jan 24 (4.3 Advanced Factoring, 10.2 Completing the Square with Circles)
• Next unit exam Fri, Jan 25 (55 minutes, in class)

Today - 4.3 Synthetic Division
Notes 

Homework
4.3 #11-21 odd

Tomorrow - 4.3 Remainder and Factor Theorems

For more information
https://www.khanacademy.org/math/algebra/polynomials/dividing_polynomials/v/synthetic-division
https://www.khanacademy.org/math/algebra/polynomials/dividing_polynomials/v/synthetic-division-example-2
https://www.khanacademy.org/math/algebra/polynomials/dividing_polynomials/v/why-synthetic-division-works
http://patrickjmt.com/synthetic-division/
http://patrickjmt.com/synthetic-division-example-2/

4.3 Long Division of Polynomials

Comic of the Day

Find the error

Quiz on 2.4 (Transformations of Radical Functions), 4.1-4.2 (Solving & Graphing Polynomials)

Warm Up
a) Determine 84÷3 by reducing the fraction, and by long division
b) Determine 85÷3 by reducing the fraction, and by long division

Announcements

• Next quiz tentatively scheduled for Thu, Jan 24 (4.3 Advanced Factoring, 10.2 Completing the Square with Circles)
• Next unit exam Fri, Jan 25 (55 minutes, in class)

Today - 4.3 Polynomial Long Division
Notes 

Homework
4.3 #1-9 odd

Tomorrow - 4.3 Synthetic Division

For more information
http://patrickjmt.com/long-division-of-polynomials/
http://patrickjmt.com/long-division-of-polynomials-a-slightly-harder-example/
https://www.khanacademy.org/math/algebra/polynomials/dividing_polynomials/v/polynomial-division
https://www.khanacademy.org/math/algebra/polynomials/dividing_polynomials/v/dividing-polynomials-1
https://www.khanacademy.org/math/algebra/polynomials/dividing_polynomials/v/dividing-polynomials-with-remainders

4.2 Intermediate Value Theorem

Comic of the Day

You: Mr. Weppler, how do polynomials work?
Me: To the internet!
PatrickJMT (videos)
Khan Academy (videos)
Wolfram Alpha (answer almost any math question)
GeoGebra (dynamic graphing calculator)

Warm Up
Graph the following.  Label the x- and y-intercepts.


Announcements

• Next quiz Thu, Jan 17 on 2.4 (Transformations of Radical Functions), 4.1-4.2 (Solving & Graphing Polynomials)
• Summary of Studying (SOS) sheet now available on Moodle http://moodle.nait.ca/mod/resource/view.php?id=834059
• Next unit exam Fri, Jan 25 (55 minutes, in class)

4.2 Intermediate Value Theorem
Notes 

Homework
4.2 #39-45 odd

Tomorrow
Pre-read 4.3 Polynomial Long Division

For more information
http://patrickjmt.com/intermediate-value-theorem/

4.2 Graphing Polynomials

Comic of the Day

Priorities...

Warm Up
a) Find the zeros of the following function:

b) Draw the graph of y=ax²+bx+c if a<0 and b²-4ac=0.  Label your x-intercepts, y-intercept and vertex.


Announcements
Next quiz Thu, Jan 17 on 2.4 (Transformations of Radical Functions), 4.1-4.2 (Solving & Graphing Polynomials)
Next unit exam Fri, Jan 25 (55 minutes, in class)

4.2 Graphing Polynomial Functions
GeoGebra applet for graphing with roots and multiplicities
http://www.geogebratube.org/student/m5519
Notes 

Homework
4.2 #1-35 don't do #37 (piecewise function)

Tomorrow
Pre-read 4.2 Intermediate Value Theorem

For more information
Math 30 Explained (need password that was e-mailed previously)

http://www.math30.ca/lessons/polynomials/polynomialFactoring/polynomialFactoring.php

4.1 Polynomial Functions

Comic of the Day

What is the ideal number of steps to graph a function?

Warm Up
Solve the following:


Return quizzes

Announcements
Next quiz Thu, Jan 17 on 4.1-4.2 Solving & Graphing Polynomials
Next unit exam Fri, Jan 25 (55 minutes, in class)

4.1 Polynomial Functions
Notes 

Homework
4.1 #23-55 odd and add #11-21 odd

Tomorrow
Pre-read 4.2 Graphing Polynomial Functions

For more information

2.4 Transformations of Radical Functions

Comic of the Day

Warm Up
Quiz.

Announcements
Assignment 1 (Getting to Know You) due on Moodle by Friday
Next quiz TBD
Next unit exam Fri, Jan 25 (55 minutes, in class)

2.4 Transformations of Radical Functions
Notes 

Homework
2.4 #67, 69 (look at handout or p. 194), 75

Tomorrow
Pre-read 4.1 Polynomial Functions

For more information
https://www.khanacademy.org/math/algebra/algebra-functions/graphing_functions/v/graphing-radical-functions

2.3 Composition of Functions

Comic of the Day

Warm Up
The circumference of a circle (using function notation) is given by C(d)=πd, where d is the diameter.  But we know that the diameter is twice the radius, or (again, using function notation), d(r)=2r.
Determine C(r), the circumference as a function of the radius.

Announcements
Assignment 1 (Getting to Know You) due on Moodle by Friday
Next quiz Fri Jan 11 (cover 1.1, 10.2, 2.2-2.4)
Next unit exam Fri, Jan 25 (55 minutes, in class)

2.3 Composition of Functions
Notes 

Homework
2.3 #1-15 odd, #39-49 odd (skip #43 & 45)

Tomorrow
Pre-read 2.4 Radical Functions (Transformations)

For more information
https://www.khanacademy.org/math/trigonometry/functions_and_graphs/function_introduction/e/functions_3

2.2 Algebra of Functions

Comic of the Day

Warm Up
Determine the value of f(2), and the value of x for f(x)=2, if:

What else could we put into f(x)?  Will it blend?

Announcements
Assignment 1 (Getting to Know You) due on Moodle by Friday
Next quiz Fri Jan 11 (cover 1.1, 10.2, 2.2-2.4)
Next unit exam Fri, Jan 25 (55 minutes, in class)

2.2 Algebra (Sum/Diff/Product/Quotient) of Functions
Notes 


Homework
2.2 #1-15 odd, add #47-51 odd


Tomorrow
Pre-read 2.3 Composition of Functions

For more information
https://www.khanacademy.org/math/trigonometry/functions_and_graphs/function_introduction/e/functions_1
https://www.khanacademy.org/math/trigonometry/functions_and_graphs/function_introduction/v/sum-of-functions
https://www.khanacademy.org/math/trigonometry/functions_and_graphs/function_introduction/v/difference-of-functions
https://www.khanacademy.org/math/trigonometry/functions_and_graphs/function_introduction/v/product-of-functions
https://www.khanacademy.org/math/trigonometry/functions_and_graphs/function_introduction/v/quotient-of-functions
https://www.khanacademy.org/math/trigonometry/functions_and_graphs/function_introduction/e/functions_2

1.1 Graphing, Distance, Midpoint & Circles

Comic of the Day

Not everything is linear...

Review Pre-Assessment (see review packages on Moodle)

Warm Up
Graph using intercepts

Expand and collect like terms


Announcements
Assignment 1 (Getting to Know You) due on Moodle by Friday
Next quiz Fri Jan 11 (cover 1.1, 10.2, 2.2-2.4)
Next unit exam Fri, Jan 25 (55 minutes, in class)

1.1 Graphing, Distance, Midpoint & Circles
GeoGuessr:
How is the distance from your guess to the actual location calculated?  What formula is used to calculate your score?
http://www.geoguessr.com/
Notes 


Homework
1.1 #35-93 odd, 10.2 #1-17 odd


Tomorrow
Pre-read 2.2 Sum/Diff/Product/Quotient of Functions

For more information
http://patrickjmt.com/the-distance-formula/
http://patrickjmt.com/the-midpoint-formula/
http://patrickjmt.com/the-center-radius-form-for-a-circle-a-few-basic-questions-example-1/
http://patrickjmt.com/finding-the-center-radius-form-of-a-circle-by-completing-the-square-example-1/
http://patrickjmt.com/quadratic-equations-completing-the-square/
http://patrickjmt.com/graphing-quadratic-functions-ex-1/

Welcome to Math 30-1!

Comic of the Day

Introduction
Meet your instructor
Team-building activity (Function Function)

Handouts
  Course Outline (general)
  Syllabus (instructor information)
  Tentative Timeline (lectures, homework, unit exams)
  Formula Sheet

Moodle (http://moodle.nait.ca)

MyMathLab (http://www.mymathlab.com)

Pre-Assessment
10 minutes, multiple-choice, NO CALCULATORS


Homework
1.1 #17-33

Tomorrow - Distance, Midpoint & Circles Formulas
Pre-read lecture notes unit 1 (available on Moodle)