Construct a rational function that has a vertical asymptote at x = 3 and a removable discontinuity at x = -2. Explain how you determined your answer.

Reggie 2021-02-11 Answered
Construct a rational function that has a vertical asymptote at x=3 and a removable discontinuity at x=2.
Explain how you determined your answer.
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

doplovif
Answered 2021-02-12 Author has 71 answers
Since x=3 is a vertical asymptote, then x3 is a factor in the denominator. Since there is a removable discontinuity at x=2, then x+2 is a common factor in the numerator and denominator. So, a possible rational function is:
f(x)=x+2(x3)(x+2)
or
f(x)=x+2x2x6
Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Relevant Questions

asked 2021-02-25
True or False. The graph of a rational function may intersect a horizontal asymptote.
asked 2020-11-05
Given that Domain of the rational function is all real numbers.
So the rational function should not contain denominator part.
asked 2022-05-26
I have been thinking of this problem recently and am wondering if anyone is able to prove/disprove it:
Let R be a rational function, that is let R ( x ) = p ( x ) / q ( x ) where p and q are polynomials of degree > 0. Assume that at some point x=a, the function R ( x ) is undefined (e.g. by division by zero): That is R ( a )undefined. Then
lim x a R ( x ) = lim x a R ( x ) ,
where R ( x ) = p ( x ) / q ( x ), where p ( x ) and q ( x ) are the derivatives of the polynomials of p and q respectively.
Is this equation always true?
asked 2020-11-05

Identify each of the following functions as polynomial, rational, algebraic, or transcendental
f(x)=2x3+3x97x2

asked 2022-02-16
Lagrange's rational function theorem states that if one has two rational functions in multiple variables f(x1,x2,xn) and g(x1,x2,xn) then one can express f as a rational function in g if and only if the set of permutations that keep g unchanged is a subset of the set of permutations that preserve f.
Is anyone familiar with the proof of this theorem? While it is fairly clear that if f can be expressed in terms of g the set of permutations that keep g unchanged has to be the subset of those that keep f unchanged, the converse is far from obvious.
asked 2022-02-16
In Hartshorne's Algebraic Geometry the function field K(Y) of a variety Y is defined as the set of equivalence classes with f being a regular function on the open subset U. We have = if f and g agree on UV.
How does one evaluate a "rational function on Y'' f? Is it f(P) using the Evaluation map for polynomials? In this case, I don't see that this is well defined: Let PUV and =, then g(P) might not even be defined!
asked 2021-06-21
True or False. Some rational functions have holes in their graph.