SOLUTION: Let f(x) be a rational function such that when f(x) is in reduced form, the numerator and denominator both have degree 3. What sorts of asymptotes could f(x) have? a. Three vertic

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Let f(x) be a rational function such that when f(x) is in reduced form, the numerator and denominator both have degree 3. What sorts of asymptotes could f(x) have? a. Three vertic      Log On


   

Question 1090612: Let f(x) be a rational function such that when f(x) is in reduced form, the numerator and denominator both have degree 3. What sorts of asymptotes could f(x) have?
a. Three vertical asymptotes only
b. One vertical asymptote and one oblique asymptote
c. One horizontal asymptote and at least one vertical asymptote
d. One horizontal and one oblique asymptote
e. No vertical asymptotes and no horizontal asymptotes
Answer by MathLover1(20855) About Me  (Show Source):
You can put this solution on YOUR website!

The graph of f(x) will have vertical asymptotes at those values of x for which the denominator is equal to zero.=> denominator could be equal to zero for one,two, or three values of x
If m=n (that is, the degrees of the numerator and denominator are the same), then the graph of f%28x%29 will have one horizontal asymptote at y=a%5Bn%5D%2Fb%5Bm%5D. (coefficients of highest degree)
When the degree of the numerator is exactly one more than the degree of the denominator, the graph of the rational function will have an oblique asymptote.
in your case, the degree of the numerator and denominator are same; so, there is no oblique asymptote
so, your answer is:
c. One horizontal asymptote and at least one vertical asymptote