determine the end behavior of the following function. y = √6 + 7x³

Explanation:

Step1: Identify the leading - term

The leading - term of the function $y=\sqrt{6}+7x^{3}$ is $7x^{3}$ since the degree of $7x^{3}$ (degree 3) is higher than the degree of the constant term $\sqrt{6}$ (degree 0).

Step2: Recall the end - behavior rule for odd - degree polynomials

For a polynomial function of the form $y = ax^{n}$ where $n$ is odd and $a>0$, as $x\to+\infty$, $y\to+\infty$ and as $x\to-\infty$, $y\to-\infty$. Here, $a = 7>0$ and $n = 3$ (odd).

Answer:

As $x\to+\infty$, $y\to+\infty$ and as $x\to-\infty$, $y\to-\infty$. The correct arrow - pair is the one with the arrow pointing down on the left and up on the right.