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Wednesday, January 11, 2006

SCRIBE POST

Today in class we continued off the notes that we did not finish off yesterday and this was what we wrote.

Many-to-one function

more than one member of the domain
is mapped to a single member of the range. (I could not upload the image because there was an error and I don't know what it is)

One-to-one function

Function where each (one) member of the domain is mapped to a unique (one) member of the range.
(same thing happened I could not do it)

Horizontal line test

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

Relations

Functions

Many-to-one---------One-to-one


A FUNCTION CAN BE LOOKED UP AS A GRAPH, EQUATION, AND TABLE OF VALUES.

One-to-one functions are "special" because they are always "invertible".

Inverse: - the inverse of any operation returns a value from its result to its original value.
- the inverse of a function "undoes" what the original function did.
Example 1:
clean room----------------------messy room }domain
BABY PLAY----------------------PARENT CLEAN-UP
messy room----------------------clean room }range

BABY PLAY and PARENT CLEAN-UP are inverses of each other. Each "undoes" what the other one "does".

NOTATION: given any function f(x) its inverse is written as f-1(x) (-1 is a power more like a square but different)
IMPORTANT: f-1(x) can not equal 1/f(x)
REMEMBER: given any function f(x) and its inverse f-1(x), the domain of f is the range of f-1 and the range of f is the domain of f-1 (see example 1)

Inverses Defined Numerically

Given any ordered pair (x,y) its inverse is (y,x). Given any function defined in a table of values, the inverse function is found by exchanging the domain and range.

Example 2:

f
x----y
(-2)--(-1)
(-1)--(1)
(0)--(3)
(1)--(5)
(2)--(7)

f-1
x----y
(-1)--(-2)
(1)--(-1)
(3)--(0)
(5)--(1)
(7)--(2)

Inverses Defined Symbolically (as equation)

1- Algebraically: to find the inverse of any function exchange the variables x and y and solve for y.

Example 3: Find the Inverse of y=2x2-3

finding the inverse
x=2y2-3
x-3=2y2
x-3/2=y2
square root of x-3/2=y

so that was it for today but the notes are unfinished and we will finish tomorrow in class.
OH YAH DON'T FORGET GraemeW CHOCOLATE BARS TOMORROW
Since GraemeW is getting chocolate bars tomorrow u can be the SCRIBE FOR TOMORROW.
HAVE FUN

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