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

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Answer 1 · 2018-05-31T21:28:44

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

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!

How do you describe the end behavior for f(x)=x^3+10x^2+32x+34f(x)=x3+10x2+32x+34f(x)=x^3+10x^2+32x+34?