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The Function Dog

The Function Dog. Putting the “Fun” in Function Since 2002 Corey Cogswell. The Function Dog. Putting the “Funk” in Function Since 2002. Wrong Funk. Right Funk. Disclaimers.

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The Function Dog

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  1. The Function Dog Putting the “Fun” in Function Since 2002 Corey Cogswell

  2. The Function Dog Putting the “Funk” in Function Since 2002

  3. Wrong Funk

  4. Right Funk

  5. Disclaimers • Gross-out math is intended for grossing out students, not teachers. If at any point during this presentation, you are offended, then it’s totally on you and your sensibilities. • This presentation is meant for purely instructional purposes and not for personal use. What that use might be, no one knows… but no judgments… • Finally, this is not intended to change your life, and if it does so, your life probably needed changing any way…

  6. Brief Biography • I graduated with a degree in mathematics from Rice University in 2002. • I have taught 8 years in Pearland ISD. • I have taught Algebra 1, Geometry, Algebra 2, SAT Prep, AMDM, PAP Precalculus, and AP Caclulus AB, and I will be adding AP Stats to that list this year. • I am currently writing a textbook for a fourth year math class, Pre-College Math, to satisfy the four by four rule. • I just began my master’s program through Lamar Academic Partnerships in Educational Technology Leadership.

  7. Brief Biography (cont.) • I understand the irony in a 2-page “brief” biography. • I am the math / speech / interview coach for Pearland’s Two-Time State Champion Academic Decathlon team. • I am a playwright in my spare time. • I dislike guacamole. • I have a Welsh corgi named Gozer the Destructor.

  8. The Evolution of the Function Dog 2006 - Present 2002 - 2005 2005 - 2006

  9. When to use the Function Dog • Order of Operations • Functions Conceptually • Function Notation • Properties • Composite Functions • Function Transformation (New for 2010) • Function Inverses (Updated for 2010) • Trigonometry • Chain Rule for Differentiation

  10. Pre-Algebra

  11. Order of Operations • Please • Excuse • My • Dear • Aunt • Sally • Parentheses • Exponents • Multiplication • Division • Addition • Subtraction

  12. Order of Operations

  13. New Order of Operations • Groupings • Exponents • Multiplication • Addition • Grandmothers • Expound • Multiple • Anecdotes • Girls • Expect • Memorized • Anniversaries • Gorillas • Eat • Mimes • Addictively

  14. Order of Operations The simplest operation one can do with two numbers is add or subtract them. 5 + 8 3

  15. Order of Operations The simplest operation one can do with two numbers is add or subtract them. 5 - 2 3

  16. Order of Operations The next simplest operation one can do with two numbers is multiply or divide them. 5 × 15 3

  17. Order of Operations The next simplest operation one can do with two numbers is multiply or divide them. 5 ÷ 3 5 3

  18. Order of Operations The most complex operation one can do with numbers (in Pre-Algebra) is applying an exponent or radical to them. 5 ^2 25

  19. Order of Operations The most complex operation one can do with numbers (in Pre-Algebra) is applying an exponent or radical to them. 25 √ 5

  20. Order of Operations The most complex dogs eat first. ^2 √

  21. Order of Operations The next most complex dogs eat second. × ÷

  22. Order of Operations The least complex dogs eat last. + -

  23. Order of Operations • Groups of dogs, or packs, can be found inside parentheses, numerators, denominators, or radicals. Packs eat before everyone else, maintaining internal pecking order. • Dogs of equal complexity eat in the order they line up.

  24. Example 1 There are four symbols in this expression and thus four dogs have lined up for dinner. Based on our rules, × will eat first followed by ÷, then +, and finally -. × 5 2 10

  25. Example 1 ÷ 5 10 2

  26. Example 1 + 2 6 4

  27. Example 1 - 6 3 3

  28. Example 2 × × 36 18 2

  29. Example 2 × 36 6 √

  30. Example 2 × 2 6 12 ÷

  31. Example 2 × 2 -1 4 5 -

  32. Example 2 × 2 -1 1 +

  33. Algebra 1

  34. Relations

  35. Functions

  36. Example 4x+5 y 17 x 3

  37. Function Notation If all functions are named y, then we run into a slight problems when there are multiple functions… y y y y y y y y y y y Which y were you looking for?

  38. Function Notation g f x g(x) f(x)

  39. Example f x 4 f(x) f(4) =3(4)2+5= 53 Input Output Coordinate: (4,53)

  40. Geometry

  41. Properties Commutative Property 3 + 8 5

  42. Properties Associative Property × ×

  43. Properties • Distributive Property 3 2 2 + × × 8 16 6 10 5

  44. Trigonometry RATIO ANGLE cos tan sin θ cos(θ) sin(θ) tan(θ)

  45. Algebra 2

  46. Composite Functions g h f f(g(h(x))) g(h(x)) h(x) x

  47. Example and g f 2 6 26 x g f

  48. External Transformations Function Transformations f x f(x)

  49. Internal Transformations Function Transformations ×b f +c x x+c f(x) b(x+c) f(b(x+c))

  50. Example 1 f x x f(2(x+5))

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