Attributes of Rational Functions

A rational function is a function that can be expressed as the quotient of two polynomials, where the denominator is not zero.

The domain of a rational function is all real numbers except where the denominator equals zero.

To find the vertical asymptote, set the denominator equal to zero and solve for x.

A horizontal asymptote is a horizontal line that the graph of a function approaches as x approaches positive or negative infinity.

1. If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is y=0. 2. If the degrees are equal, the horizontal asymptote is y = leading coefficient of numerator / leading coefficient of denominator.

X-intercepts are points where the graph of the function crosses the x-axis, found by setting the numerator equal to zero.

Y-intercepts are points where the graph of the function crosses the y-axis, found by evaluating the function at x=0.

An asymptote is an imaginary line that a graph approaches but never touches.

Vertical asymptotes indicate values of x where the function is undefined and the graph tends to infinity.

Horizontal asymptotes indicate the behavior of the function as x approaches infinity or negative infinity.