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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
[tex]2x^4+17x^3+20x^2-75x[/tex]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
[tex]as\text{ x }\rightarrow\infty,f(x)\rightarrow+\infty[/tex]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
[tex]as\text{ x}\rightarrow-\infty,f(x)\rightarrow+\infty[/tex]Answer2:
[tex]\begin{gathered} \text{as x}\rightarrow+\infty,f(x)\rightarrow+\infty \\ as\text{ x}\rightarrow-\infty,f(x)\rightarrow+\infty \end{gathered}[/tex]