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Chosen as the EXCLUSIVE publisher for the new Pre-Calculus Grade 11& 12 courses Opening Doors! Calgary Teacher’s Convention February 16, 2012

Table of Contents Unit 1: Transformations and Functions – Chapter 1: Function Transformations – Chapter 2: Radical Functions – Chapter 3: Polynomial Functions Unit 2: Trigonometry – Chapter 4: Trigonometry and the Unit Circle – Chapter 5: Trigonometric Functions and Graphs – Chapter 6: Trigonometric Identities Unit 3: Exponential and Logarithm Functions – Chapter 7: Exponential Functions – Chapter 8: Logarithmic Functions Unit 4: Equations and Functions – Chapter 9: Rational Functions – Chapter 10: Function Operations – Chapter 11: Permutations, Combinations, and the Binomial Theorem

Unit Unit Opener Unit Project Chapters (2 or 3 per unit) Sections (3 to 5 per chapter) Investigate Link the Ideas Check Your Understanding Chapter Review Practice Test Unit Project Wrap-Up Cumulative Review Unit Test 3-Part Lesson

Math 30-1 Possible Course Outline September 2012 – January 2013 ChapterNumber of DaysTentative Exam Date Function Transformations8September 13 Radical Functions6September 21 Polynomial Functions8October 3 Trig and the Unit Circle8October 16 Trig Functions and Graphs8October 26 Trig Identities8November 6 Exponential Functions6November 16 Log Functions7November 27 Rational Functions6December 5 Function Operations6December 13 Perms/Combs6December 21

Pre-Calculus 12, McGraw-Hill Ryerson Chapter 1 Transformations 1.1 8R Kennedy

A variable y is said to be a function of a variable x if there is a relation between x and y such that every value of x corresponds to one and only one value of y. What is a Function? The symbol ‘ f (x) ’ may be used to denote a function of x. For example, 4x + 5 is the function of x. It can be expressed as f(x) = 4x + 5. or Besides x, we can have functions of other variables, for example, is a function of u and we may write The letter ‘f ’ in the symbol ‘f(x)’ can be replaced by other letters, for example, 9R Kennedy

Functions linear quadratic absolute value square root cube root cubic reciprocal exponential logarithmic sine Graphs of Functions 10R Kennedy cosine Line Dance

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y = |x|+ 8 y = |x| – 8 Graph Translations of the Form y – k = f(x) Given the graph of y = |x|, graph the functions y = |x| + 8 and y = |x| – 8. The transformed graphs are congruent to the graph of y = |x|. Each point (x, y) on the graph of y = |x| is transformed to become the point (x, y + 8) on the graph of y = |x| + 8. Ex: (–4, 4)  (–4, 12) It becomes the point (x, y – 8) on the graph of y = |x| – 8. Ex: (–4, 4)  (–4, -4) (-4, 4) (-4, 12) (-4, -4) 12R Kennedy

Graphing y = f(x) + k x –8 –6 –4 – y = |x| y = |x| The graph of a function is translated vertically if a constant is either added or subtracted from the original function. Each point (x, y) on the graph of y = |x| is transformed to become the point (x, y + 8) on the graph of y – 8 = |x|. Using mapping notation, (x, y) → (x, y + 8). Graph y = |x| R Kennedy

y = |x + 7| y = |x - 8| Graph Translations of the Form y = f(x – h) Given the graph of y = |x|, graph the functions y = |x + 7| and y = |x – 8|. The transformed graphs are congruent to the graph of y = |x|. Each point (x, y) on the graph of y = |x| is transformed to become the point (x – 7, y) on the graph of y = |x + 7|. Ex: (–4, 4)  (–11, 4) It becomes the point (x + 8, y) on the graph of y = |x – 8|. Ex: (–4, 4)  (4, 4) (-4, 4) (-11, 4) (4, 4) 14R Kennedy

Horizontal and Vertical Translations Sketch the graph of y = |x – 4|– 3. Apply the horizontal translation of 4 units to the right to obtain the graph of y = |x – 4|. Apply the vertical translation of 3 units down to y = |x – 4| to obtain the graph of y = |x – 4| – 3. y = |x – 4| – 3 y = |x – 4| The point (0, 0) on the function y = |x| is transformed to become the point (4, -3). In general, the transformation can be described as (x, y) → (x + 4, y – 3). (0, 0) (4, -3) 15R Kennedy

Given the function defined by a table Determine the coordinates of the following transformations x–3–2–10123 f(x)f(x) f(x) + 3 f(x + 1) f(x – 2) + 4 Transformation of functions y – k = f(x – h) (0, 6)(–3, 10)(–2, 7)(–1, 12)(1, 15)(2, 8)(3, 9) (–1, 3)(–4, 7)(–3, 4)(–2, 9)(–2, 12)(–3, 5)(–4, 6) (2, 7)(–1, 11)(0, 8)(1, 13)(3, 16)(4, 9)(5, 10) Each point (x, y) on the graph of y = f(x)is transformed to become the point (x + h, y + k) on the graph of y – k = f(x – h). Using mapping notation, (x, y) → (x + h, y + k). 16R Kennedy

Transformation of functions y – k = f(x – h) Possible Assignment Essential: #1 – 3, 5, 6, 8, 10 – 12, C1, C2, C4 Typical: #5, 7 – 12, 13 or 14, C1, C2, C4 Enrichment #15 – 19, C2 – C4 17R Kennedy

What might emerge if we let kid loose to work on anything they want for a day with the only proviso that their presentation the next day explain: why they had undertaken this work, how it used or connected with math and what they had done? There is an Australian software company called Atlassian and they do something once a quarter where they say to their software developers: You can work on anything you want, any way you want, with whomever you want, you just have to show the results to the rest of the company at the end of 24 hours. They call these things Fed-Ex Days, because they basically have to deliver something overnight. That one day of intense autonomy has produced a whole array of software fixes, a whole array of ideas for new products, and a whole array of upgrades for existing products