Key Features of Rational Functions

Front

x-intercept

Back

Set numerator equal to zero after simplifying

Front

y-intercept

Back

Plug in zero for x after simplifying

Front

Vertical asymptote

Back

Set denominator equal to zero after simplifying

Front

horizontal asymptote

Back

Compare degrees of numerator and denominator

Front

x-value of hole

Back

Set cancelled out factor equal to zero

Front

y-value of hole

Back

Plug x-value of hole into simplified equation

Front

If degree of numerator is GREATER THAN degree of denominator, the horizontal asymptote is...

Back

N/A - there isn't one

Front

If degree of numerator is LESS THAN degree of denominator, the horizontal asymptote is...

Back

y = 0

Front

If degree of numerator is EQUAL TO degree of denominator, the horizontal asymptote is...

Back

y = the ratio of leading coefficients