pre-cal 40s march 4, 2009

11
Baby Play or All About Inverse Functions duck wrangling by toyfoto

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Vertical and horizontal reflections and inverse functions.

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Page 1: Pre-Cal 40S March 4, 2009

Baby Playor

All About Inverse

Functions

duck wrangling by toyfoto

Page 2: Pre-Cal 40S March 4, 2009

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

g(x) = x + 3x3ƒ(x) = x + 2x + 324

Page 3: Pre-Cal 40S March 4, 2009

ƒ is an even function.COMPLETE THE GRAPH.

Page 4: Pre-Cal 40S March 4, 2009

ƒ is an odd function.COMPLETE THE GRAPH.

Page 5: Pre-Cal 40S March 4, 2009

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

Reflections

Page 6: Pre-Cal 40S March 4, 2009

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

Page 7: Pre-Cal 40S March 4, 2009

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

Page 8: Pre-Cal 40S March 4, 2009

Baby Playor

All About Inverse

Functions

duck wrangling by toyfoto

Page 9: Pre-Cal 40S March 4, 2009

Inverses ...The concept ...

Numerically speaking ...

Page 10: Pre-Cal 40S March 4, 2009

Inverses ...Algebraically speaking ...

Conceptually analyzing the function ...

Page 11: Pre-Cal 40S March 4, 2009

Inverses ...

Graphically speaking ...