SOLUTION: Find an expression for a rational function ƒ(x) that satisfies the conditions: a horizontal asymptote at y = 100, vertical asymptotes at x = 0 and x = 1, and contains the point (6,

Algebra ->  Rational-functions -> SOLUTION: Find an expression for a rational function ƒ(x) that satisfies the conditions: a horizontal asymptote at y = 100, vertical asymptotes at x = 0 and x = 1, and contains the point (6,      Log On


   

Question 878234: Find an expression for a rational function ƒ(x) that satisfies the conditions: a horizontal asymptote at y = 100, vertical asymptotes at x = 0 and x = 1, and contains the point (6, 2).
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Something like y=100x%2F%28x%2B7%29 will approach 100 as x either increases or decreases without bound. Any such y=100x%2F%28x%2Bk%29 for some constant k will also approach 100. That helps you understand the horizontal asymptote you want.

Your vertical asymptote specification means you must have denominator with factors x and (x-1). You could use this to begin forming the rational function, y=100x%2F%28x%28x-1%29%29 but this is not yet finished. Notice that you will not have your needed y=100 for large x.

? Try y=%28100x%2B1%29%28x%2B1%29%2F%28x%28x-1%29%29 arbitrarily picking the "plus one" just so as not to interfere with the vertical asymptotes. This is still not ready. You must yet form the function to include (6,2).