1.2 Graphs of Functions

In section 1.2 the class discussed even and odd functions.  Functions can be even, odd, or neither and there is multiple ways to determine this.  A function can be tested for evenness and oddness algebraically or graphically.

A function f is even if, for each x in the domain of f, f (-x) = f (x).

A function f is odd if, for each x in the domain of f, f (-x) = - f (x).

A function is neither even or odd when neither of the above is true.

Reminder: It is very important that you understand and remember the definitions of both even and odd functions.

Graphical Solutions

Even Functions

If the graph of a function is symmetric with respect to the y-axis, the function is even.

Examples:

 Odd Functions

If the graph of a function is symmetric with respect to the origin, the function is odd.

Examples: 

Algebraic Solutions Examples

Is this function even, odd or neither? 

In this case f (-x) = f (x) so the function is even and no more work is necessary.

Is this function even, odd or neither? 

f (-x) doesn't equal f (x) so we check to see if f (-x) = -f (x).

This function is odd because f (-x) = -f (x).

Sources:

Sources for graphs: http://www.dummies.com/how-to/content/how-to-interpret-function-graphs.html

http://sophia.hccs.edu/~susan.fife/1314/GraphsofBasicFunctions.htm

Other information found in textbook.  (Precalculus with Limits A Graphing Approach).
Helpful website: purplemath