SOLUTION: Write a rational function with a vertical asymptote x=5 and horizontal asymptote y=1/2. I have no clue where to begin.

Algebra ->  Rational-functions -> SOLUTION: Write a rational function with a vertical asymptote x=5 and horizontal asymptote y=1/2. I have no clue where to begin.      Log On


   

Question 811469: Write a rational function with a vertical asymptote x=5 and horizontal asymptote y=1/2. I have no clue where to begin.
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Imagine the degree of numerator is equal to that of the denominator, and that one of the expression or factors in the denominator is (x-5).

Try something simple, %28x-5%29%28x-1%2F2%29%2F%28x-5%29. Seeing the way the denominator is chosen, x=5 will be a vertical asymptote. This will NOT give the horizontal asymptote wanted; so try a change.

highlight%28x%28x-5%29%2F%28%28x-5%29%282x%29%29%29
Still the same x=5 vertical asymptote. Also there is now x=0 vertical asymptote. Note what would happen as x is increased without bound... The x in numerator and denominator would cancel as 1, and the x-5 in numerator and denominator would cancel as 1, and the expression would approach (1/2), being y=1%2F2 as horizontal asymptote.