Notes inverse.pdf

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Unit 1

Inverses

Quick Review of Functions

Functions has three parts

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Domain:

Range:

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Graph of a Function: Vertical Line Test

To be a function, a line can

only intersect a graph of a function ( )

o

. IF it touches more than

function.

Determine if it is a function…

Examples: Determine if it is a Function???

1.

2.

3.

4.

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Examples: Determine if it is a Function??? 1 0 2 3 4 5 6 7 8 9 10 1 2 3 4 5 1

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Key Concept

Inverse of a Function

Relation

Inverse

Inverse of a Function –

is formed when the

I

variable is with

the

e

variable. of

the x and y values. Inverses are indicated by the

notation .

Example:

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OnetoOne Function

Horizontal Line Test

One to

and only

e

output.

Example

Not

If

no

horizontal line

intersects the graph

of a

function more than

once,

then the

inverse

of

is a function.

In order for the

inverse of a function

to be a

function, the

original function

must be a

onetoone

function and meets the criteria for

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Examples: Determine if the function is one to one ?

1.

2.

3.

4.

5.

6.

7.

8.

Not all

functions

meet the

criteria

to have an

inverse

which is also a

function.

However, if the

domain is restricted (example:

) , only

part of

the domain

is used, then the inverse will be a

function.

Example: Is one to one?

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Example:

Is onetoone a function?

Vertical Line test:

Horizontal Line test:

What was restricted to make it a function?

If the function turns the apple into a banana

Then the

inverse

function turns the banana back

to the apple

Description of an Inverse

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Mathematical operational pairs

(What operation undoes the other)

Addition (+)

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Example:

We have a function machine.

We need to decide

what function

can be used to make the output the

same as the input number.

Describe the

operation symbolically.

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2.

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5.

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Function notation to know that you are looking

at an inverse

How to find inverse for functions…..

Mathematical

Operational Method

Algebraic method

1. Let

2.

Interchange x and y

variables

3. Solve for y

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1. Find the inverse of the function ?

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What is the inverse of

1.

2.

3.

4.

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Graphs of inverse relations

The graph of an

relationship is the

of the about the

line .

Point .

What is the inverse?

Point .

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Write the inverse function for the table of values. Graph the function in black and in a different color on the coordinate grid at the right. Then graph the line of reflection for the corresponding points.

Is a function also?

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Example:

Use the graph below to draw the graph of

the inverse function. What are the domain and range for

the inverse function

The accompanying diagram

represents the graph of f(x)

Which graph represents

1.

2.

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Composition of Inverse Function

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Original Inverse

Vertex

Graph and its inverse