A rational function is a function that can be expressed as a ratio of two polynomials. It can also be written in the form f(x) = P(x) / Q(x), where P(x) and Q(x) are polynomials.
To evaluate the limit of a rational function, you can use the factoring and cancellation method. First, factor both the numerator and denominator. Then, cancel out any common factors. Finally, plug in the limit value to see what the result is. If it is undefined, then the limit does not exist.
The horizontal asymptote of a rational function can be found by looking at the degree of the numerator and denominator. If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is y = 0. If the degrees are equal, divide the leading coefficients to find the horizontal asymptote. If the degree of the numerator is greater than the degree of the denominator, there is no horizontal asymptote.
Yes, a rational function can have multiple vertical asymptotes. This occurs when there are zeros in the denominator of the function that cause the function to be undefined at those points.
A rational function is continuous at a certain point if the limit of the function exists at that point and is equal to the value of the function at that point. If the limit does not exist or is not equal to the function value at that point, then the function is discontinuous at that point.