Question

How do you write the end behaviour of a polynomial? if the polynomial is 2x^4+17x^3+20x^2-75x what are the end behaviours?

Answer 1

End behavior

Answer1. 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 - ∞).

For the polynomial

`2x^4+17x^3+20x^2-75x`

The end behaviors

The graph for the function is

Consider this graph of the polynomial function. Notice that as you move to the right on the x-axis the graph of the function goes up. We can describe the end behavior symbolically by writing

`as\text{ x }\rightarrow\infty,f(x)\rightarrow+\infty`

On the other end of the graph, as we move to the left along the x-axis, the graph of the function goes up, too. We can describe the end behavior symbolically by writing

`as\text{ x}\rightarrow-\infty,f(x)\rightarrow+\infty`

Answer2:

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