Question

How do you describe the end behavior of `y=(x+1)(x-2)([x^2]-3)`?

Answer 1

See explanation.

Explanation:

[x^2] forms the sequence {n^2), with the limit `oo`, as `xtto +-oo`.

`y = x^2 [x^2] (1+1/x)(1-2/x)(1-3/([x^2])) to oo`, as `x to +-oo`.

Piecewise, the graph is a series of arcs of parabolas, with holes at

ends.

For example,

`y= (x+1)(x-2)(-1), x in [sqrt2, sqrt3)`, giving

`(x-1/2)^2=-(y-9/4)`

The size of a typical parabola, `a = 1/(4( [n^2]-3)) to 0`, as x to oo#.

The center `to (1/2, -oo)`, on the common axis `x = 1/2`.

The arcs drift away from the common axis x = 1/2.

I have done some research for giving details. I would review, and if

necessary, revise my answer, later.