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Pre-Cal 40S March 4, 2009
 

Pre-Cal 40S March 4, 2009

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Vertical and horizontal reflections and inverse functions.

Vertical and horizontal reflections and inverse functions.

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    Pre-Cal 40S March 4, 2009 Pre-Cal 40S March 4, 2009 Presentation Transcript

    • Baby Play or All About Inverse Functions duck wrangling by toyfoto
    • Are these functions even or odd? Justify your answers algebraically. 3 g(x) = x + 3x 4 ƒ(x) = x + 2x + 3 2
    • ƒ is an even function. COMPLETE THE GRAPH.
    • ƒ is an odd function. COMPLETE THE GRAPH.
    • Reflections I thought I saw a puddy cat.... by flickr user law_keven
    • Reflections Vertical Reflections Given any function ƒ(x): • ƒ(x) produces a reflection in the x-axis. y-coordinates are multiplied by (-1) Horizontal Reflections Given any function ƒ(x): • ƒ(-x) produces a reflection in the y-axis. x-coordinates are multiplied by (-1) Inverses: the inverse of any function ƒ(x) is (read as: quot;EFF INVERSEquot;) WARNING: undoes whatever ƒ did. Zuiderkerk by flickr user MorBCN
    • Reflections Vertical Reflections Given any function ƒ(x): • ƒ(x) produces a reflection in the x-axis. y-coordinates are multiplied by (-1) Horizontal Reflections Given any function ƒ(x): • ƒ(-x) produces a reflection in the y-axis. x-coordinates are multiplied by (-1) Inverses: the inverse of any function ƒ(x) is (read as: quot;EFF INVERSEquot;) WARNING: undoes whatever ƒ did. Zuiderkerk by flickr user MorBCN
    • Baby Play or All About Inverse Functions duck wrangling by toyfoto
    • Inverses ... The concept ... Numerically speaking ...
    • Inverses ... Conceptually analyzing Algebraically speaking ... the function ...
    • Inverses ... Graphically speaking ...