1 Answer

Kishor Kumar Rawat · Answer 1 · 2019-06-26T09:57:43+0000

The leading term of polynomial function is the the term contain highest degree so here in the given question leading term is
-3x^5

and leading coefficient is the coefficient of the term with greatest exponent -3

RULES for End behaviour

we have following four cases

CASE1: 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

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

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

CASE3: 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

$x\rightarrow -\infty$
$x\rightarrow \infty$

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

Here in the given case we have odd degree and negative leading coefficient

$x\rightarrow -\infty$
$x\rightarrow -\infty$

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

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