Pre-Cal 40S March 4, 2009

Post on 29-Nov-2014

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Vertical and horizontal reflections and inverse functions.

transcript

Baby Playor

All About Inverse

Functions

duck wrangling by toyfoto

Are these functions even or odd? Justify your answers algebraically.

g(x) = x + 3x3ƒ(x) = x + 2x + 324

ƒ is an even function.COMPLETE THE GRAPH.

ƒ is an odd function.COMPLETE THE GRAPH.

I thought I saw a puddy cat.... by flickr user law_keven

Reflections

Vertical ReflectionsGiven any function ƒ(x):• ƒ(x) produces a reflection in the x-axis.y-coordinates are multiplied by (-1)

WARNING:

undoes whatever ƒ did.

Inverses: the inverse of any function ƒ(x) is (read as: "EFF INVERSE")

Horizontal ReflectionsGiven any function ƒ(x):• ƒ(-x) produces a reflection in the y-axis.x-coordinates are multiplied by (-1)

Reflections

Zuiderkerk by flickr user MorBCN

Vertical ReflectionsGiven any function ƒ(x):• ƒ(x) produces a reflection in the x-axis.y-coordinates are multiplied by (-1)

WARNING:

undoes whatever ƒ did.

Inverses: the inverse of any function ƒ(x) is (read as: "EFF INVERSE")

Horizontal ReflectionsGiven any function ƒ(x):• ƒ(-x) produces a reflection in the y-axis.x-coordinates are multiplied by (-1)

Reflections

Zuiderkerk by flickr user MorBCN

Baby Playor

All About Inverse

Functions

duck wrangling by toyfoto

Inverses ...The concept ...

Numerically speaking ...

Inverses ...Algebraically speaking ...

Conceptually analyzing the function ...

Inverses ...

Graphically speaking ...