Pre-Cal 30S January 9, 2009

10
Baby Play or All About Inverse Functions duck wrangling by toyfoto

description

Inverse functions.

Transcript of Pre-Cal 30S January 9, 2009

Page 1: Pre-Cal 30S January 9, 2009

Baby Playor

All About Inverse

Functions

duck wrangling by toyfoto

Page 2: Pre-Cal 30S January 9, 2009

For each of the following functions, identify the inner function g(x) and the outer function F(x).

Chain Linkage

Page 3: Pre-Cal 30S January 9, 2009

Many-to-one functionMore than one member of the domain is mapped to a single member of the range.

1

4

9

-2

5

http://fooplot.com

-2

mapping

outputinputdomain range

Page 4: Pre-Cal 30S January 9, 2009

Function where each (one) member of the domain is mapped to a unique (one) member of the range.

One-to-one function

1

4

9

-2

5

7

http://fooplot.com

Page 5: Pre-Cal 30S January 9, 2009

Used only on the graphs of functions. (i.e the vertical line test has already been satisfied).

Horizontal line test

Sweep a horizontal line across the graph of any function if the line crosses the graph more than once the function is many-to-one if the line crosses the graph everywhere exactly once then the function is one-to-one.

Page 6: Pre-Cal 30S January 9, 2009

Baby Playor

All About Inverse

Functions

duck wrangling by toyfoto

Page 7: Pre-Cal 30S January 9, 2009

Inverses ...The concept ...

Numerically speaking ...

Page 8: Pre-Cal 30S January 9, 2009

Inverses ...Algebraically speaking ...

Conceptually analyzing the function ...

Page 9: Pre-Cal 30S January 9, 2009

Inverses ...

Graphically speaking ...

Page 10: Pre-Cal 30S January 9, 2009

Find the inverse:

-2-1012

127-350

x y-2-1012

127-350

x y