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nasty-shy [4]
3 years ago
5

considering the leading term of the polynomial function. what is the end behavior of the graph? describe the end behavior and pr

ovide the leading term. -3x^5+9x^4+5x^3+3
Mathematics
1 answer:
mario62 [17]3 years ago
3 0

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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