Question

What is the end behavior of the function?

Answer 1

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 2

Answer:

$\text{As }x\rightarrow -\infty, f(x)\rightarrow +\infty$

$\text{As }x\rightarrow +\infty, f(x)\rightarrow -\infty$

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,

$\text{As }x\rightarrow -\infty, f(x)\rightarrow +\infty$

$\text{As }x\rightarrow +\infty, f(x)\rightarrow +\infty$

If the degree = even and leading coefficient = negative,

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

$\text{As }x\rightarrow +\infty, f(x)\rightarrow -\infty$

If the degree = odd and leading coefficient = positive,

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

$\text{As }x\rightarrow +\infty, f(x)\rightarrow +\infty$

If the degree = odd and leading coefficient = negative,

$\text{As }x\rightarrow -\infty, f(x)\rightarrow +\infty$

$\text{As }x\rightarrow +\infty, f(x)\rightarrow -\infty$

Here, the given polynomial,

$f(x) = -2x^5 + 5x^3 - 2x + 13$

Since, 5 = odd and -2 = negative,

Hence, the end behaviour of the polynomial,

$\text{As }x\rightarrow -\infty, f(x)\rightarrow +\infty$

$\text{As }x\rightarrow +\infty, f(x)\rightarrow -\infty$