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

Question

asked Jun 7, 2018 142k views

2 Answers

Vadim Belyaev · Answer 1 · 2018-06-14T11:38:49+0000

Answer: Option 4 is correct

Step-by-step 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