What are holes in rational functions?
HoleA hole exists on the graph of a rational function at any input value that causes both the numerator and denominator of the function to be equal to zero.
Rational FunctionA rational function is any function that can be written as the ratio of two polynomial functions.
How do you find the asymptotes and holes of a rational function?
Set each factor in the denominator equal to zero and solve for the variable. If this factor does not appear in the numerator, then it is a vertical asymptote of the equation. If it does appear in the numerator, then it is a hole in the equation.
How do you know if it’s a hole or vertical asymptote?
Identifying vertical, horizontal asymptotes and holes –
Which asymptotes are determined by looking at the denominator?
The horizontal asymptote of a rational function can be determined by looking at the degrees of the numerator and denominator. Degree of numerator is less than degree of denominator: horizontal asymptote at y = 0.