Key Concepts in Rational Functions

Front

Domain

Back

Everything in the denominator of the factored version.

Front

Vertical Asymptotes

Back

Zeros of the denominator but not zeros of the numerator; look at the denominator of the reduced form.

Front

x-intercepts

Back

Zeros of the numerator but not zeros of the denominator; look at the numerator of the reduced form; a (x, 0) point.

Front

y-intercept

Back

The ratio of the constants of the numerator/denominator in reduced form, and (0, y) point.

Front

Horizontal Asymptotes

Back

Option 1: When the degree of the denominator is bigger than the degree of the numerator, always y = 0.

Option 2: When the degrees of the numerator and the denominator are equal, always

y = ratio of the leading term numerator/denominator.

Front

Slant Asymptotes

Back

When the degree of the numerator is bigger than the degree of the denominator; y = mx + b, find using long division.

Front

Hole

Back

When a factor cancels out; a zero in the numerator that is also in the denominator; find the value of the zero that cancels out and substitute it into the reduced form of the function; always a (x, y) point.