What is the end behavior of $f (x) = x^{5} + 2 x^{2}$ $f(x)=x^5+2x^2$ ?

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Answer 1 · 2017-07-04T20:04:33

See the explanation below.

First, graph the function.
graph{x^5 + 2x^2 [-10, 10, -5, 5]}

You can see that as $x \to \infty, f (x) \to \infty$ $x -> oo, f(x)->oo$ .
As $x \to - \infty, f (x) \to - \infty$ $x->-oo, f(x)->-oo$ .

You can also write this in limit notation:

$lim_(x->oo) f(x) = oo$

$lim_(x->-oo) f(x) = -oo$

What is the end behavior of f(x)=x^5+2x^2f(x)=x5+2x2f(x)=x^5+2x^2?