Respuesta :
The degree of the function is 3, so it's odd. The leading coefficient is 2, so it's positive. Therefore, the end behavior of the graph of the functions is:
as x approaches negative infinity, f(x) approaches negative infinity
as x approaches positive infinity, f(x) approaches positive infinity
as x approaches negative infinity, f(x) approaches negative infinity
as x approaches positive infinity, f(x) approaches positive infinity
The end behavior of a polynomial function is the behavior of the graph of as approaches positive infinity or negative infinity. The degree and the leading coefficient of a polynomial function determine the end behavior of the graph.
Degree - 3 (odd);
Leading coefficient - 2 (positive).
Then
- when [tex]x\rightarrow -\infty,[/tex] then [tex]f(x)\rightarrow -\infty;[/tex]
- when [tex]x\rightarrow \infty,[/tex] then [tex]f(x)\rightarrow \infty.[/tex]
See attached graph of the function for graphical illustration.
