Ask y = ax + B / X (Nike function) when a, B different sign of the range and image?

It's not very clear to ask questions about images in words
a. B different sign, there are two cases, in fact, are similar
I'm going to talk about one of them, and I'll make an analogy with the other
a> 0 B0
The image is similar to y = lgx, but the intersection point with X axis is not 1

Nike function problem
What are the properties of y = x + 1 / x? What are the vertices, the domain of definition and the range of values

Check function

Y = max {2x, X & # 178;} x ∈ [0,4] piecewise function form

Let x ^ 2 = 2x,
The solution is x = 0 or x = 2
When we know that x belongs to [0,2], x ^ 2-2x = x (X-2) < 0, that is, x ^ 2 < 2x,
When x belongs to [2,4], x ^ 2-2x = x (X-2) > 0, that is, x ^ 2 > 2x,
so
2X x belongs to [0,2]
y=max｛2x,x²｝=｛
X ^ 2 x belongs to [2,4]

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Ask y = ax + B / X (Nike function) when a, B different sign of the range and image?