Recheck that result you get from "setting the denominator to 0 and using the quadratic formula to find the roots".CallMeShady said:Homework Statement
Homework Equations
None
The Attempt at a Solution
I was able to find a vertical asymptote at x=-3/8 by setting the denominator to 0 and using the quadratic formula to find the roots. However, I am unsure of how to find the horizontal asymptotes, and I am not 100% confident that my vertical asymptote is correct. The confusion that I have here is with the square root in the denominator.
SammyS said:
A horizontal asymptote is a horizontal line that a curve approaches but never touches as the x-values of the curve approach positive or negative infinity. It represents the long-term behavior of the curve.
To find the horizontal asymptote of a curve, you need to look at the highest degree terms in the numerator and denominator of the function. If the degree of the numerator is greater than the degree of the denominator, then there is no horizontal asymptote. If the degrees are equal, the horizontal asymptote is the ratio of the leading coefficients. If the degree of the denominator is greater than the degree of the numerator, the horizontal asymptote is y = 0.
A vertical asymptote is a vertical line that a curve approaches but never touches as the x-value of the curve approaches a specific value. It represents a value at which the function is undefined.
To find the vertical asymptote of a curve, you need to look for any values of x that make the denominator of the function equal to 0. These values will be the x-coordinates of the vertical asymptotes. You should also check for any removable discontinuities by simplifying the function.
Yes, a curve can have multiple horizontal and/or vertical asymptotes. This can occur when the function has multiple terms with the same highest degree in the numerator or denominator, or when there are multiple values that make the denominator equal to 0.