Doug C. answered • 07/30/18

Math Tutor with Reputation to make difficult concepts understandable

Create the "hole" at x= 5 by introducing a factor of (x-5) in both numerator and denominator of rational function.

Do create a vertical asymptote at x=-6, introduce a factor of (x+6) in the denominator.

In order to have a horizontal asymptote at y=7 the reduced function (after the (x-5) factors are cancelled) must approach 7 as x->∞ (or -∞). An example of that would be y = 7x/(x+6), or (7x-3)/(x+6), etc.

https://www.desmos.com/calculator/fr2gzdocr3

See the above graph for an example.