Respuesta :
The leading term of polynomial function is the the term contain highest degree so here in the given question leading term is [tex]-3x^5[/tex]
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
[tex]x\rightarrow -\infty[/tex] [tex]f(x)\rightarrow \infty[/tex]
[tex]x\rightarrow \infty[/tex] [tex]f(x)\rightarrow \infty[/tex]
CASE2: Even degree and negative leading coefficient
[tex]x\rightarrow -\infty[/tex] [tex]f(x)\rightarrow -\infty[/tex]
[tex]x\rightarrow \infty[/tex] [tex]f(x)\rightarrow -\infty[/tex]
CASE3: Odd degree and positive leading coefficient
[tex]x\rightarrow -\infty[/tex] [tex]f(x)\rightarrow -\infty[/tex]
[tex]x\rightarrow \infty[/tex] [tex]f(x)\rightarrow \infty[/tex]
CASE4: Odd degree and negative leading coefficient
[tex]x\rightarrow -\infty[/tex] [tex]x\rightarrow \infty[/tex]
[tex]x\rightarrow \infty[/tex] [tex]f(x)\rightarrow -\infty[/tex]
Here in the given case we have odd degree and negative leading coefficient
[tex]x\rightarrow -\infty[/tex] [tex]x\rightarrow -\infty[/tex]
[tex]x\rightarrow \infty[/tex] [tex]f(x)\rightarrow -\infty[/tex]
