 ## Tutoring on The Properties of Functions

Learning Objectives:

#### Understand to find the Sum, Difference,Product and Quotient of a Function.

Math Tutoring on The Properties of Functions

If we let f and g be functions and x is in the domain of both,
1)  (f + g )( x ) =  f ( x ) + g ( x )

2)  (f - g )( x )  =  f ( x ) - g ( x )
3)  ( f x g) ( x ) = f ( x) x g ( x )

4)  ( f/ g )( x ) = f ( x ) / g( x )

There are two main ways to determine if a Function is Even or Odd. One is an algebraic method, and the other is a graphical method.

A function is Even if algebraically, f ( x )  = f ( -x ) and graphically the graph has symmetry across the y axis. A polynomial function will have all even exponents on the variables. For odd functions algebraically, -f (x)  =  f ( -x) and graphically the graph has rotational symmetry, about the origin, which means the graph remains the same after a rotation of 1800. A polynomial function that is odd will have all odd exponents on the variable.

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Hook Questions:

1.    What are the basic properties of function?

2.    When is a function even?

3.    Define an odd function.

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