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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1. What are the basic properties of function?
2. When is a function even?
3. Define an odd function.
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