SOLUTION: Write the equation of a possible rational function with the following characteristics: - vertical asymptotes at x=3 and x=-3 - x intercepts of x=5 and x=-1

SOLUTION: Write the equation of a possible rational function with the following characteristics: - vertical asymptotes at x=3 and x=-3 - x intercepts of x=5 and x=-1 - horizontal asympto

Question 960100: Write the equation of a possible rational function with the following characteristics:
- vertical asymptotes at x=3 and x=-3
- x intercepts of x=5 and x=-1
- horizontal asymptote of y=1/2
I started with: y=(x+3)/(x-5)/(x+3)(x-3)
My final answer for the question is y=(2x^2-8x-10)/(x^2-9)
I am not sure if my answer is correct and I am also unclear as to where the horizontal asymptote should be placed into the equation.
Answer by josgarithmetic(39620) (Show Source): You can put this solution on YOUR website!
Information for better guidance:

x-intercepts are the same as ROOTS or ZEROS for the function, which appear in the numerator. Think, "binomial factors".

Horizontal asymptote means that the degree of numerator and denominator are equal.

You correctly chose degree two for numerator and denominator. The horizontal asymptote means that the leading terms of numerator and denominator become increasingly important as x goes to the left or the right unbounded, and the ratio of their coefficients will approach .

That should be enough to make the proper adjustments. You almost have it.
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