Question

I am trying to find the vertical asymptote equation for g(x)= -log(x) +2

Answer 1

g(x) = -log(x), has a vertical asymptote at x=0, where g(x)= + infinity. Adding 2 to this does not change anything. Note that this asymptote is one-sided, it goes up to infinity on the positive side of the x-axis, as x goes to 0, but does not come down on the other side, because log(x) is not defined for negative values of x.

Answer 2

This is what I have for my answers Vertical Asymptote equation is x = 0
Vertical shift up 2 units and a reflection of the x-axis
(x, y) form (100,0)
is there no actual equation then for the vertical Asymptote?

Answer 3

@stoopkid

Answer 4

Well, generally you don't use an "actual equation", as you say, for these kinds of problems, because you'd have to have infinity somewhere in your equation, and its just not that well-defined. The trick is to find those values of your function which aren't defined, (i.e. where the function goes to + or - infinity). If you had a "rational function" i.e. a polynomial over another polynomial, then you would solve for the zeroes of the polynomial in the denominator, and this would give you those x-values which give you a 0 in the denominator. Since you can't divide by 0, these x-values will cause your rational function to go to + or - infinity. It's a little bit more complicated than that, because not EVERY zero will give you an asymptote, but that's the jist of it. In your situation though, log(x) has a more complicated definition and the best way to go about this is to just know where its asymptote is and why. If you want me to explain further then @me again.

Answer 5

thanks a lot, that was defiantly a great explanation and I think I am good now!! Thanks again.