Describe the end behavior of the graph for each function. f(x)=x^3+2x^2-5x+1

Question

anonymous · Answer

End behavior can be described by the limits$$\lim_{x\to\pm\infty}f(x)$$

samsan9 · Answer

what about g(x)=-2x^3-8x^2+18x+72=0

samsan9 · Answer

@SithsAndGiggles

anonymous · Answer

The procedure is the same. 

For example, directly substituting, you have
$$\lim_{x\to-\infty}g(x)=-2(-\infty)^3-8(-\infty)^2+18(\infty)+72=+\infty_1-\infty_2+\infty_3$$
Now, $\infty-\infty$ isn't properly defined. This is why I used different subscripts to denote different $\infty$s. In this case, since $x^3$ increases faster than $x^2$, the $\infty$ from the first term $(-2x^3)$ dominates the $\infty$ from the second term $(-8x^2)$, which means that $\infty_1>\infty_2$, so $\infty_1-\infty_2=\infty$.

So, the limit as $x\to-\infty $ of $g(x)$ is $+\infty$. Does this make sense?

samsan9 · Answer

well ill take a picture and read through it to make sure :) thank you

anonymous · Answer

np