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Pre-Cal 40S March 4, 2009

on Mar 04, 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, 2009Presentation 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 ...