Chosen as the EXCLUSIVE publisher for the new Pre-Calculus Grade 11& 12 courses

1. R Kennedy

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

3. http://www.mcgrawhill.ca/school/tr/7D052003

4. http://learning.arpdc.ab.ca/

5. 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 Table of Contents

6. 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

7. Math 30-1 Possible Course Outline September 2012 – January 2013

8. Chapter 1 Transformations 1.1 Horizontal and Vertical Translations R Kennedy Pre-Calculus 12, McGraw-Hill Ryerson

9. or Besides x, we can have functions of other variables, for example, is a function of u and we may write What is a Function? 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. 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. The letter ‘f ’ in the symbol ‘f(x)’ can be replaced by other letters, for example, R Kennedy

10. reciprocal logarithmic linear sine cubic exponential quadratic absolute value cube root square root Functions cosine Line Dance Graphs of Functions R Kennedy 1.1.2

11. R Kennedy

12. 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. y = |x|+ 8 (-4, 12) 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) (-4, 4) y = |x| – 8 (-4, -4) It becomes the point (x, y – 8) on the graph of y = |x| – 8. Ex: (–4, 4)  (–4, -4) R Kennedy

13. Graph y = |x| + 8 Graphing y = f(x) + k 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). R Kennedy

14. 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|. (-11, 4) 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) (-4, 4) (4, 4) y = |x - 8| y = |x + 7| It becomes the point (x + 8, y) on the graph of y = |x – 8|. Ex: (–4, 4)  (4, 4) R Kennedy

15. Horizontal and Vertical Translations Sketch the graph of y = |x –4|– 3. (0, 0) (4, -3) • Apply the horizontal translation of 4 units to the right to obtain the graph of y = |x – 4|. y = |x – 4| • Apply the vertical translation of 3 units down to y = |x – 4| to obtain the graph of y = |x – 4| – 3. 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). y = |x – 4| – 3 R Kennedy

16. Transformation of functions y – k = f(x – h) • Given the functiondefined by a table • Determine the coordinates of the following transformations (–3, 10) (–2, 7) (–1, 12) (0, 6) (1, 15) (2, 8) (3, 9) (–4, 7) (–3, 4) (–2, 9) (–1, 3) (–2, 12) (–3, 5) (–4, 6) (–1, 11) (0, 8) (1, 13) (2, 7) (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). R Kennedy

17. 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 R Kennedy

18. 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 • 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?