SOLUTION: Write the equation of a rational function that has: - real zeros when x = 1 and 2 - a removable discontinuity when x = 3 - a vertical asymptote when x = 4

SOLUTION: Write the equation of a rational function that has: - real zeros when x = 1 and 2 - a removable discontinuity when x = 3 - a vertical asymptote when x = 4 - a horizontal as

Question 1168760: Write the equation of a rational function that has:
- real zeros when x = 1 and 2
- a removable discontinuity when x = 3
- a vertical asymptote when x = 4
- a horizontal asymptote at y = 3
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
needs (x-3)/(x-3) for the discontinuity.
(x-1)(x-2) in the numerator for the roots
(x-4) in the denominator for the asymptote
3 in the numerator and another term with x in the denominator so that the power of the numerator and denominator are both the same to give the asymptote of 3. I used (x-4), since it did not affect the roots or the hole.
3(x-1)(x-2)(x-3)/(x-3)(x-4)^2

RELATED QUESTIONS
Create a function y=f(x) that has a removable discontinuity at x=2 and a non-removable... (answered by greenestamps)

Construct a rational function that has a vertical asymptote at x=3 and a removable... (answered by josgarithmetic)

Can someone help? Tank you. Find the equation of rational function f(x) with a... (answered by solver91311)

what function has a removable discontinuity at... (answered by jim_thompson5910)

Which of the following is true for F(x) = (x^(2)+9)/(x-3)? A) There is a removable... (answered by Boreal,Edwin McCravy)

Find the removable discontinuity of the rational function:... (answered by josgarithmetic)

Let f be the function defined by f(x)=(cx-(5x^2))/((2x^2)+ax+b), where a, b, and c are... (answered by solver91311)

Consider g(x) = 2x^3 - x^2 + 2x -1 (a) Tell the maximum number of real zeros that the... (answered by greenestamps)

Is the function f(x)=|x|/x continuous?_____ If not continuous, a) At what value of x... (answered by jim_thompson5910)