
Nathan B. answered 03/24/15
Tutor
5
(20)
Elementary and Algebraic skilled
5 - 1 =4
4/2 = 2
That is, there is a span of 4 units between the two asymptotes, which means there graph has to have two units to expand out to. So we have 2x in the numerator.
(1+5)/2 = 6/2 = 3
3 is the midway point between our asymptotes, so we can add that as our 'b', if we were looking at this like a linear equation.
We can't just have √x2 in the denominator, else we're going to have essentially x/±x, and that wouldn't give us an asymptote. So we add an inconsequential number to have it hug and give us the curve, like 1:
√(x2 +1)
We add all the pieces together, and we have a graph that looks like:
y = 2x/√(x2 +1) + 3