Can you have a slant and horizontal asymptote?
Hereof, can a function cross a slant asymptote?
NOTE: A common mistake that students make is to think that a graph cannot cross a slant or horizontal asymptote. This is not the case! A graph CAN cross slant and horizontal asymptotes (sometimes more than once). It's those vertical asymptote critters that a graph cannot cross.
One may also ask, what are the rules for horizontal asymptotes? The three rules that horizontal asymptotes follow are based on the degree of the numerator, n, and the degree of the denominator, m.
- If n < m, the horizontal asymptote is y = 0.
- If n = m, the horizontal asymptote is y = a/b.
- If n > m, there is no horizontal asymptote.
Also Know, what is the equation of the horizontal or oblique asymptote?
Case 1: If the degree of the numerator of f(x) is less than the degree of the denominator, i.e. f(x) is a proper rational function, the x-axis (y = 0) will be the horizontal asymptote. The line y = mx + b is an oblique asymptote for the graph of f(x), if f(x) gets close to mx + b as x gets really large or really small.
Why do slant asymptotes occur?
A slant (oblique) asymptote occurs when the polynomial in the numerator is a higher degree than the polynomial in the denominator. To find the slant asymptote you must divide the numerator by the denominator using either long division or synthetic division.