Discriminant: 

If 

two real solutions 

If 

one real solution (double solution) 

If 

two imaginary solutions 
Circles: 
A Circle with center at 

and radius 



If 

, then 

Even and Odd Functions: (symmetry) 

If 

the function is even 

Even functions are symmetric to the YAxis 



If 

the function is odd 

Odd functions are symmetric to the Origin 



A function can be neither even or odd 
Permutations and Combinations: 




Asymptotes: 

Horizontal Asymptotes: (exponents) 


(top is bigger) 
No H. A. 



(same) use coef. 




(bottom is bigger) 



Vertical Asymptotes 


(set Denominator equal to zero) 

Slant Asymptotes 


(top is exactly one more than bottom) 


Use long division to obtain 


Descarte's Rule of Signs: 

The number of positive zeros is equal to the number of 

sign variations in 

, or is less than the number 

by an even integer. 


The number of negative zeros is equal to the number of 

sign variations in 

, or is less than the number 

by an even integer. 


(imaginary numbers come in pairs) 

Rational Zero Theorem: 



Remainder Theorem: 

If 

is divided by 

, the remainder is 


Compound Interest: 



Continuously Compounded Interest: 



Present Value: 



Binomial Expansion Formula: 





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