Question

How do you describe the end behavior for `f(x)=x^3+10x^2+32x+34`?

Answer 1

`lim_(xtooo) f(x)=oo, lim_(xto-oo) f(x)=-oo`

Explanation:

To find the end behavior of this function, we can evaluate its limits at positive and negative infinity.

In `f(x)`, the term with the highest exponent will dominate the end behavior, so we can evaluate the limit of those. We have

`lim_(xtooo) x^3=oo`

As `x` gets very large, the exponent will just make it balloon. The value will stay positive.

`lim_(xto-oo) x^3=-oo`

As `x` gets very negative, the function will go towards negative infinity, because of the odd exponent.

Hope this helps!