Can a graph of a rational function have no vertical asymptote?
In respect to this, what function does not have a vertical asymptote?
Since the denominator has no zeroes, then there are no vertical asymptotes and the domain is "all x". Since the degree is greater in the denominator than in the numerator, the y-values will be dragged down to the x-axis and the horizontal asymptote is therefore "y = 0".
Furthermore, how do you find vertical asymptotes and holes? 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.
In this manner, how do you know if a rational function has a vertical asymptote or not?
Finding Vertical Asymptotes of Rational Functions. An asymptote is a line that the graph of a function approaches but never touches. The curves approach these asymptotes but never cross them. To find the vertical asymptote(s) of a rational function, simply set the denominator equal to 0 and solve for x.
How do you find the asymptotes of a function?
Finding Horizontal Asymptotes of Rational Functions
- If both polynomials are the same degree, divide the coefficients of the highest degree terms.
- If the polynomial in the numerator is a lower degree than the denominator, the x-axis (y = 0) is the horizontal asymptote.