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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.

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