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

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(20850) (Show Source): You can put this solution on YOUR website!

The graph of f(x) will have vertical asymptotes at those values of for which the is equal to zero.=> could be equal to zero for ,, or values of
If (that is, the degrees of the numerator and denominator are the same), then the graph of will have horizontal asymptote at . (coefficients of highest degree)
When the degree of the numerator is exactly 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

RELATED QUESTIONS
Let F(x) be the real-valued function defined for all real x except for x = 1 and x = 2... (answered by CPhill,ikleyn)

Let f(x)be a polynomial function of degree 2 and g(x) be a polynomial of degree 3. what... (answered by josgarithmetic)

Let f(x) be a polynomial such that f(0) = 4, f(1) = 6, and f(2) = -2. Find the remainder (answered by math_tutor2020)

Find a polynomial f(x) of degree 5 such that both of these properties hold: * f(x) is... (answered by CPhill)

Let f be a function such that f(-1) = 3 and f(2) = -4. The coordinates of two points on... (answered by Edwin McCravy)

Let f be a linear function such that f(2) = 17 and f(-1/3) = 3. What is... (answered by ewatrrr)

Let f be a function such that f(0)=2 and f’ (x)<_6 for -10<_x<_10. 1) what is the... (answered by ikleyn)

O.k so I have this rational function f(x)=x^2-x-2/4x+8, I am having trouble finding the... (answered by Boreal)

Let X be F distributed with 9 numerator and 12 denominator degrees of freedom. Find :... (answered by CPhill)