Question

Which of the following best describes the end behavior of this polynomial function?

Answer 1

we can rewrite your polynomial function as below:
\[y = {x^4}\left( {a + \frac{b}{x} + \frac{c}{{{x^2}}} + \frac{d}{{{x^3}}} + \frac{e}{{{x^4}}}} \right)\]
now if x goes to +infinity or -infinity, then the sum inside the parentheses goes to a

Answer 2

and: \(a\cdot x^4\) goes to +infinity, being \(a>0\)

Answer 3

I see that B. and C. have positive infinity

Answer 4

f(x) never goes to -infinity

Answer 5

Oh I see so that would make it choice B. then because C. goes to - infinity

Answer 6

correct! the right option is B

Answer 7

@Michele_Laino Ok thank you so when a > 0 (greater sigh) it can only go to positive infinity and in a < 0 (less than) it can go to negative infinity?

Answer 8

if \(a<0\) your polynomial function goes to -infinity, in both cases as x goes to +infinity or to -infinity

Answer 9

Ok thank you :)

Answer 10

:)