Ch 1.2 Graph of Functions

 

Even and Odd Functions

A graph has symmetry with respect to the y-axis if when ever points (x,y) and (-x,y) are both on the graph. This is usually a even function.

 

A graph has symmetry with respect to the origin if when ever points (x,y) and (-x,-y) are both on the graph. This is usually a odd function.

Ex. (1)

      

  

 

Even function, symmetry to the y-axis, (x,y) and (-x,y)

 



 

Ex. (2)

   

 



Odd function, symmetry to origin, (x,y) and (-x,-y)





 

 

 

A function f is increasing on an interval if, for any x1 and x2 in the interval,

 implies

 

 

A function f is decreasing on an interval if, for any x1 and x2 in the interval,

 implies

 

 

A function value f(a) is called a relative maximum of f if there exists n interval (x1,x2) that contains a such that



 implies

 

A function value f(a) is called a relative minimum of f if there exists n interval (x1,x2) that contains a such that

 

 implies