Question

What is the end behavior of the function?f(x) = 2x^7 − 5x^3 − 2x + 1Enter your answer by filling in the boxes.As x→−∞, f(x)→As x→∞, f(x)→

Answer 1

`\begin{gathered} As\text{ }x\rightarrow-\infty,f(x)\rightarrow-\infty \\ As\text{ }x\rightarrow\infty,f(x)\rightarrow\infty \end{gathered}`

Step-by-step explanation:

Given:

`f\mleft(x\mright)=2x^7−5x^3−2x+1`

Recall that the end behavior of a polynomial depends on the sign of the leading coefficient, which is the coefficient of the highest degree variable, and the degree of the polynomial.

From the given polynomial, we can see that the degree is 7(odd) and the leading coefficient is 2(positive).

Since this polynomial has a degree that is odd and a positive leading coefficient, its end behavior will be;

`\begin{gathered} As\text{ }x\rightarrow-\infty,f(x)\rightarrow-\infty \\ As\text{ }x\rightarrow\infty,f(x)\rightarrow\infty \end{gathered}`