Question

What is the end behavior of `f(x) = x^2`?

Answer 1

`lim_(x to+-oo) x^2=oo`

Explanation:

Whenever we think about end behavior, we want to think about what our function approaches as it goes to positive and negative infinity.

To think about this, we can take the limit of our function as `x` approaches `+-oo`.

`lim_(x tooo) x^2=oo`

Since we have an even exponent, `x` will always be positive and just get ridiculously large, and rather quickly.

`lim_(xto-oo) x^2=oo`

Once again, the even exponent will always make the term positive even if our `x` is negative. It will also balloon up rather quickly.

Hope this helps!