Question

1. Which of the following describes the end behavior of the function ƒ(x) = x^4 + 3x^3 – 2x + 7?

Answer 1

Hello, when x tends to $\infty$ the term with the highest degree will lead the behaviour.

In other words.

$\displaystyle \lim_{x\rightarrow+\infty} {x^4+3x^3-2x+7}\\\\=\lim_{x\rightarrow+\infty} {x^4}\\\\=+\infty\\\\\\\displaystyle \lim_{x\rightarrow-\infty} {x^4+3x^3-2x+7}\\\\=\lim_{x\rightarrow-\infty} {x^4}\\\\=+\infty$

So, the answer B is correct.

Thank you.