HM2 C Block 3.2.16
March 02, 2016
Objectives:
1) Determine algebraically whether a
function is even, odd or neither
2) Describe the symmetry in the graph of an
even or odd function
Even Function: An even function is symmetric about the yaxis.
Examples:
HM2 C Block 3.2.16
March 02, 2016
Properties of Even Functions:
If the point (x, y) is on the graph, then the point (-x, y) is on
the graph.
Example:
If a function is an even function, the following
statement is true:
f(-x)=f(x)
Example: Prove that f(x)=x2 is an even function
HM2 C Block 3.2.16
Odd Function: An odd function is symmetric about origin
(rotational symmetry 180 degrees).
Examples:
Properties of Odd Functions:
If the point (x, y) is on the graph, then the point (-x, -y) is on
the graph.
Example:
March 02, 2016
HM2 C Block 3.2.16
March 02, 2016
If a function is an odd function, the following statement is true:
f(-x) = -f(x)
Example: Prove that f(x)=x3 is an odd function
Example: Determine whether the function is either, odd or
neither:
HM2 C Block 3.2.16
March 02, 2016