Question

For the polynomial f(X)=2x^3-9x^2+11x-20AsX -> -♾️,f(X) -> ♾️, calculate the end behavior

Answer 1

Answer:

The polynomial is given below as

$f(x)=2x^3-9x^2+11x-20$

Definition of end behavior:

The end behavior of a function f describes the behavior of the graph of the function at the "ends" of the x-axis. In other words, the end behavior of a function describes the trend of the graph if we look to the right end of the x-axis (as x approaches +∞ ) and to the left end of the x-axis (as x approaches −∞ ).

Step 1:

Figure out the domain of the function

The domain of a function is the set of all possible inputs for the function. For example, the domain of f(x)=x² is all real numbers, and the domain of g(x)=1/x is all real numbers except for x=0.

$\begin{gathered} f(x)=2x^3-9x^2+11x-20 \\ the\text{ domain of the function is given below as} \\ -\inftyStep 2:

Limit the polynomial to -∞ and +∞

[tex]\begin{gathered} \lim_{x\to\infty}f(x)=2x^3-9x^2+11x-20=\infty \\ as\text{ x}\rightarrow+\infty,f(x)\rightarrow+\infty \end{gathered}$$\begin{gathered} \lim_{x\to-\infty}f(x)=2x^3-9x^2+11x-20=-\infty \\ as\text{ x}\rightarrow-\infty,f(x)\rightarrow-\infty \end{gathered}$

Hence,

The end behavior of the polynomial is given below as

$\begin{gathered} as\text{ x}\rightarrow+\infty,f(x)\rightarrow+\infty \\ as\text{ x}\rightarrow-\infty,f(x)\rightarrow-\infty \end{gathered}$