To find horizontal asymptotes: If the degree (the largest exponent) of the denominator is bigger than the degree of the numerator, the horizontal asymptote is the x-axis (y = 0). If the degree of the numerator is bigger than the denominator, there is no horizontal asymptote.
How do you know if a horizontal asymptote exists?
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.
- Degree of numerator is greater than degree of denominator by one: no horizontal asymptote; slant asymptote.
Why do horizontal asymptotes occur?
An asymptote is a line that a graph approaches without touching. Similarly, horizontal asymptotes occur because y can come close to a value, but can never equal that value. The graph of a function may have several vertical asymptotes. ...
