Question

Select the graph and the description of the end behavior of f(x) = −x3 − 2.

Answer 1

The answer is the fourth one

Answer 2

Answer:  Option 4 is correct

Explanation:

End behaviour of graph can be check by following rules

Case 1: even degree  and positive leading coefficient

$x\rightarrow -\infty$        $f(x)\rightarrow \infty$

$x\rightarrow \infty$          $f(x)\rightarrow \infty$

Case2: Even degree and negative leading coefficient

$x\rightarrow -\infty$          $f(x)\rightarrow -\infty$

$x\rightarrow \infty$            $f(x)\rightarrow -\infty$

Case 3: odd degree and positive leading coefficient

$x\rightarrow -\infty$            $f(x)\rightarrow -\infty$

$x\rightarrow \infty$            $f(x)\rightarrow \infty$

Case4: Odd degree and negative leading coefficient

$x\rightarrow -\infty$            $f(x)\rightarrow \infty$

$x\rightarrow \infty$              $f(x)\rightarrow -\infty$

Here we have a case of odd degree and negative leading coefficient  here when $x\rightarrow -\infty$            $f(x)\rightarrow \infty$

$x\rightarrow \infty$                  $f(x)\rightarrow -\infty$

Hence, Option 4 is correct