Answer:
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.
Answer:
See Explanation
Step-by-step explanation:
In a rational equation, horizontal asymptotes are based on the highest degree of the polynomials on the numerator and denominator.
If it is top-heavy (higher degree on the numerator), then there is no asymptote.
Ex: [tex]\frac{x^{6} +4}{x^{3} +3}[/tex]. The degree of the numerator is 6 and the denominator degree is 3; 6>3, so no asymptote.
If it is bottom-heavy (higher degree on denominator), then the x-axis (y=0) is the horizontal asymptote.
Ex: [tex]\frac{x^{2}+x+5 }{x^{5}-3}[/tex]. The highest degree of the numerator is 2 vs the highest degree of 5 on the denominator. Thus, the equation is bottom-heavy and the asymptote is at 0.
If the degrees are the same, you take the coefficient of the variables with the highest degrees and then divide.
Ex. [tex]\frac{6x^{2}-3x+1}{2x^{2}+3}[/tex]. Take the coefficients of the x^2 (which is the highest degree variable). You should get 6 and 2. And then divide them in order to get:
y=6/2 = 3
