Math- Rational Functions
Functions with Fractions
How to find vertical asymptotes
Look for the values which make the function undefined. Presented as 'X='
How to find horizontal asymptotes
When the degree of the denominator is D and the degree of the numerator is N, if..
N = D, then Y=A/B
N < D, then Y=O
N > D, then there is no horizontal asymptote
How to find x-intercept
Solve for whichever values make the numerator equal to zero. Presented as a ' (X,0) '
How to find y-intercept
Solve the equation when all X equal zero. Presented as a ' (0,Y) '
How to find domain
All values except those which make the denominator equal zero.
How to find range
All values except those lying on horizontal asymptotes.
How to find a hole
A number which is a factor in both the numerator and the denominator.
How to find a slant asymptote
If the numerator's degree is one higher than the denominator's (ex: 2x⁴ / 19x³+2 ) then divide out the problem using long division. The answer, sans remainder, is the asymptote.