SOLUTION: Create a function which has the following properties: 1. It has a horizontal asymptote at y=2 2. It has a discontinuity at x=2 which is not a vertical asymptote 3. It has no oth

Algebra ->  Rational-functions -> SOLUTION: Create a function which has the following properties: 1. It has a horizontal asymptote at y=2 2. It has a discontinuity at x=2 which is not a vertical asymptote 3. It has no oth      Log On


   

Question 993143: Create a function which has the following properties:
1. It has a horizontal asymptote at y=2
2. It has a discontinuity at x=2 which is not a vertical asymptote
3. It has no other discontinuities or asymptotes
Explain, in detail, why each of the properties is satisfied by your example. Full marks will not be given if there is any doubt in your explanation that you completely understand why the conditions are satisfies.
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
a%28x-r%29%5E2%2F%28x-2%29%5E2
Not yet sure of the factor, a, but at least the only possible hole is at x=2; but not yet right unless numerator has this same binomial factor as denominator.

a%28x-2%29%2F%28x-2%29
Degree of numerator and denominator are same, and degree not need to be greater than 1.

2%28x-2%29%2F%28x-2%29
The constant factor is 2, making sure that the horizontal asymptote is y=2; which the line IS REACHED. No vertical asymptote; just the hole at x=2.