Inequalities
 Solve inequalities to get numbers and look for terms that make system undefined to find
cut-off points
 Find working areas by plugging in numbers to the equation from each section and
checking to see if they work
 Can use calculator Solver function to find cutoff points with difficult equations
Absolute Value
 Set absolute value side of the equation equal to the + and – of the other side to find
answers
 If inequalities, find cutoff points again and test all the areas
Limits
 Can input a number very close to the one being approached and see what the limit
comes out to be
Asymptotes
 If you can reduce the equation, then the undefined tells you you have an asymptote
 If you have an equation that you can’t reduce then the undefined tell you you have a
removable discontinuity
 To find horizontal asymptote, solve for x and isolate x’s/y’s
 If your approaching infinity, then you will have a horizontal asymptote
 If your limit is infinity then you will have a vertical asymptote
Symmetry
 Replace x in the equations with –x. If the signs are opposite then it is symmetrical to the
y-axis
 Replace y in the equations with –y. If the signs are the same then it is symmetrical over
the x-axis
 Replace both x and y with –x and –y. If the signs are opposite then it is symmetrical to
the origin
Continuous
 Show it is continuous by showing that they have the same limit, and also by plugging in
the limit to the equation and getting the same answer in each