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3 years ago

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Mathematics

1 answer:

hichkok12 [17]3 years ago

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Answer:

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Step-by-step explanation:

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Analyze the end behavior of each function below. Then, choose one of the functions, and explain how you determined

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End behavior of a polynomial function depended on the degree and its leading coefficient.

1. If degree is even and leading coefficient is positive then

$p(x)\rightarrow \infty\text{ as }x\rightarrow \infty$

$p(x)\rightarrow \infty\text{ as }x\rightarrow -\infty$

2. If degree is even and leading coefficient is negative then

$p(x)\rightarrow -\infty\text{ as }x\rightarrow \infty$

$p(x)\rightarrow -\infty\text{ as }x\rightarrow -\infty$

3. If degree is odd and leading coefficient is positive then

$p(x)\rightarrow \infty\text{ as }x\rightarrow \infty$

$p(x)\rightarrow -\infty\text{ as }x\rightarrow -\infty$

4. If degree is odd and leading coefficient is negative then

$p(x)\rightarrow -\infty\text{ as }x\rightarrow \infty$

$p(x)\rightarrow \infty\text{ as }x\rightarrow -\infty$

(a)

$f(x)=x^4$

Here, degree is even and leading coefficient is positive.

$f(x)\rightarrow \infty\text{ as }x\rightarrow \infty$

$f(x)\rightarrow \infty\text{ as }x\rightarrow -\infty$

(b)

$g(x)=-x^4$

Here, degree is even and leading coefficient is negative.

$g(x)\rightarrow -\infty\text{ as }x\rightarrow \infty$

$g(x)\rightarrow -\infty\text{ as }x\rightarrow -\infty$

(c)

$h(x)=x^3$

Here, degree is odd and leading coefficient is positive.

$h(x)\rightarrow \infty\text{ as }x\rightarrow \infty$

$h(x)\rightarrow -\infty\text{ as }x\rightarrow -\infty$

(d)

$k(x)=-x^3$

Here, degree is odd and leading coefficient is negative.

$k(x)\rightarrow -\infty\text{ as }x\rightarrow \infty$

$k(x)\rightarrow \infty\text{ as }x\rightarrow -\infty$

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3 years ago