Chapter 1

                                                                     Chapter 1 

Book's definition of a Function
               - A set of relation that matches each item from one set with exactly one item from a different set.


                                                              Even Functions definition  

How can you recognize whether or not a function is even based on its graph?

-The graph is symmetrical about the Y-axis

Example: 

This Graph is an Even function because it reflexes on the Y-axis  

How to decide whether if an equation is and even function?

Example:

We want to know this the equation above is an even function. you know the definition on and even function is 

so now you would put the input of the -x in the x position 

 And now salve from here

Now that F(-x) = F(x) you know its an even function 

Odd Function definition 

How can you recognize whether or not a function is odd based on its graph?

- Its symmetrical about the origin 

Example:

This graph is and odd function because it reflexes off the origin  

How to tell if an equation is an odd function?

Example: 

    

 Simplify                                                                                                                 Simplify

                                                                                                      

                       The Two equation equal each other and there for the equation is and odd function  

ONE-TO-ONE definition 

If......Then

How can you recognize whether or not a function is one-to-one based on its graph?

- it passes the horizontal line test 

This graph is a one-to-one function because it passes the horizontal line test.

How to tell if an equation is an one-to-one function?

Example: 

Now set the equation above equal to each other and plug in a on one said and b on the other said and see if they a become equal 

Now simplify

because a and b are equal to each other show that this equation is a one-to-one function 

Inverse Function definition 

If F&G are inverse, then (Fog)(x) = x

What is the relationship between the graph of a function and the graph of its inverse?

- there reflex across each other

The kinda function that has and inverse is a one-to-one function. 

Example: 

Fine the inverse of

Now change the F(x) top y 

Now change the x and the y and solve for y

And this is the inverse!!