Question

The function f(x) = 7x-m/2-nx, find the values of m and n such that the vertical asymptote is x=6, and the x-intercept is 5.

Answer 1

The function is f(x)= (7x-m)/(2-nx)
the vertical asymptote is x=6, that means 2/n = 6 or n=1/3

And now, we have f(x)=(7x-m):(2-1/3x)= (14x-2m): (6-x)

the x-intercept is 5 and we have y=0, x=5. So we obtain 0=(70-2m):(6-5)
or 70-2m=0, m=35

Conclusion m=35 and n=1/3