Question

What is the end behavior of the graph of the polynomial function f(x) = 2x3 – 26x – 24?

Answer 1

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 $x\rightarrow -\infty,$ then $f(x)\rightarrow -\infty;$
• when $x\rightarrow \infty,$ then $f(x)\rightarrow \infty.$

See attached graph of the function for graphical illustration.

Answer 2

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