horizontal asymptotes

Question

Find the point where the graph of f crosses its horizontal asymptote

f(x)= 6x(x-4)/ (x-5)(x+6)

Answer 1

f(x) = 6x(x - 4)/(x - 5)(x + 6).

Horizontal asymptote is y = 6. So, f(x) = 6; 6x(x - 4)/(x - 5)(x + 6) = 6; x² - 4x = x² + x - 30;

1. 5x = - 30; x = 6. So, point is (6, 6)

Answer 2

First, we need to find where the horizontal asymptote is. To do this, we take the limit of the function as x→∞. Since this is a rational function, the limit is the ratio of the coefficients of the highest degree. This is 6/1, or 6.

Now we need to know what x value will give us an f(x) of 6. To do this, we set up the equation as:

6x(x-4) / ((x-5)(x+6)) = 6

And solve for x. Simplifying this equation gives us x = 6. Thus, the point at which this function crosses its horizontal asymptote is (6,6).

Answer 3

Please see video. :-)