Pre-Cal 40S Slides March 3, 2008
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Pre-Cal 40S Slides March 3, 2008

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Inverse functions: 4 perspectives.

Inverse functions: 4 perspectives.

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Pre-Cal 40S Slides March 3, 2008 Presentation Transcript

  • 1. Baby Play or All About Inverse Functions duck wrangling by toyfoto
  • 2. EVEN FUNCTIONS Graphically: A function is quot;evenquot; if its graph is symmetrical about the y-axis. These functions are even... These are not ... Symbolically (Algebraically) a function is quot;evenquot; IFF (if and only if) ƒ(-x) = ƒ(x) Examples: Are these functions even? 1. f(x) = x² 2. g(x) = x² + 2x f(-x) = (-x)² g(-x) = (-x)² + 2(-x) f(-x) = x² g(-x) = x² - 2x since f(-x)=f(x) since g(-x) is not equal to g(x) f is an even function g is not an even function
  • 3. ODD FUNCTIONS Graphically: A function is quot;oddquot; if its graph is symmetrical about the origin. These functions These are are odd ... not ... Symbolically (Algebraically) a function is quot;oddquot; IFF (if and only if) ƒ(-x) = -ƒ(x) 1. ƒ(x) = x³ - x 2. g(x) = x³- x² Examples: ƒ(-x) = (-x)³ - (-x) g(-x) = (-x)³ - (-x)² ƒ(x) = -x³ + x g(x) = -x³ - x² -ƒ(x) = -(x³ - x) -g(x) = -(x³-x²) -ƒ(x) = -x³ + x -g(x) = -x³+ x² since ƒ(-x)= -ƒ(x) since g(-x) is not equal to -g(x) ƒ is an odd function g is not an odd function
  • 4. Are these functions even or odd? Justify your answers algebraically. g(x) = x3+ 3x ƒ(x) = x4+ 2x2+ 3
  • 5. ƒ is an odd function. COMPLETE THE GRAPH.
  • 6. Baby Play or All About Inverse Functions duck wrangling by toyfoto
  • 7. Inverses ... The concept ... Numerically speaking ...
  • 8. Inverses ... Algebraically speaking ... Conceptually analyzing the function ...
  • 9. Inverses ... Graphically speaking ...