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What is the end behavior of the function?

f(x)=−2x5+5x3−2x+12

Enter your answer by filling in the boxes.

As x→−∞ , f(x)→

As x→∞ , f(x)→

What is the end behavior of the function fx2x55x32x12 Enter your answer by filling in the boxes As x fx As x fx class=

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abnerjoseperez

Answer:

X->-infinite, graph is positive +(infinite)

X-> + infinite, graph is negative (-infinite)

Step-by-step explanation:

When you study end behaviour of a polynomial, you verify it's highest exponent. If it is odd, like this exercise, it's Y values come from negative infinity to positive infinity. If the coefficient is negative, it is the opposite, it comes from positive infinite to negative infinite.

Answer:

[tex]\text{As }x\rightarrow -\infty, f(x)\rightarrow +\infty[/tex]

[tex]\text{As }x\rightarrow +\infty, f(x)\rightarrow -\infty[/tex]

Step-by-step explanation:

Since, the end behaviour of a polynomial f(x) depends upon the leading coefficient ( coefficient of higher degree variable ) and degree of the polynomial,

If the degree = even and leading coefficient = positive,

[tex]\text{As }x\rightarrow -\infty, f(x)\rightarrow +\infty[/tex]

[tex]\text{As }x\rightarrow +\infty, f(x)\rightarrow +\infty[/tex]

If the degree = even and leading coefficient = negative,

[tex]\text{As }x\rightarrow -\infty, f(x)\rightarrow -\infty[/tex]

[tex]\text{As }x\rightarrow +\infty, f(x)\rightarrow -\infty[/tex]

If the degree = odd and leading coefficient = positive,

[tex]\text{As }x\rightarrow -\infty, f(x)\rightarrow -\infty[/tex]

[tex]\text{As }x\rightarrow +\infty, f(x)\rightarrow +\infty[/tex]

If the degree = odd and leading coefficient = negative,

[tex]\text{As }x\rightarrow -\infty, f(x)\rightarrow +\infty[/tex]

[tex]\text{As }x\rightarrow +\infty, f(x)\rightarrow -\infty[/tex]

Here, the given polynomial,

[tex]f(x) = -2x^5 + 5x^3 - 2x + 13[/tex]

Since, 5 = odd and -2 = negative,

Hence, the end behaviour of the polynomial,

[tex]\text{As }x\rightarrow -\infty, f(x)\rightarrow +\infty[/tex]

[tex]\text{As }x\rightarrow +\infty, f(x)\rightarrow -\infty[/tex]

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