Functions
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graphically testing symmetry
 xaxis: for every point (x,y) there is (x,y)
 yaxis: for every point (x,y) there is (x,y)
 origin: for every point (x,y) there is (x,y)

algebraically testing symmetry
 xaxis: replace y by y, equivalent equation should result
 yaxis: replace x by x, equivalent equation should result
 origin: replace x by x and y by y, equivalent equation should result

average rate of change equation

difference quotient equation

algebraically knowing whether a graph is odd, even, or neither
 even: f(x)=f(x); plug in x and you should get original equation
 odd: f(x)=f(x); plug in x and you should get the opposite equation

graphically knowing whether a graph is odd, even, or neither
 even graphs have yaxis symmetry
 odd graphs have origin symmetry

how to graph piecewise functions
 graph each piece and keep only the part in the interval
 use open circles and closed circles accordingly