Functions are bounded, unbounded, convergent, divergent, with and without limits. What are the relations between these relations?

If a function is monotonically bounded, it must have a limit, and if there is a limit, it must converge
There is no limit to the divergence of unbounded functions
If it's convenient, I'll check the gaoshu book. It's very detailed

Given that f (x) is a quadratic function, the vertex of its image is (1,3), and it passes through the origin, find f (x)

By vertex
f(x)=a(x-1)²+3
Over origin
x=0,y=0
0=a(0-1)²+3
a=-3
f(x)=-3x²+6x

Let f (x) = {x ^ 2 + 2x + 1, X ≤ 1, x, 1

f(1)=4≠1
Therefore, the limit does not exist when x → 1
f(2)=2=2
lim(x→2)f(x)=2
im(x→3.5)f(x)=5

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