To determine which graph shows a polynomial function f, such that
- [tex]f(x)\rightarrow \infty,[/tex] when [tex]x\rightarrow -\infty;[/tex]
- [tex]f(x)\rightarrow \infty,[/tex] when [tex]x\rightarrow \infty,[/tex]
you have to find the graph that is
- decreasing when x are infinitely small;
- increasing, when x are infinitely large.
Consider all options:
A. When x are infinitely small, the graph is decreasing and when x are infinitely large, the graph is decreasing too. Thus, this option is false.
B. When x are infinitely small, the graph is increasing. So, this option is false.
C. When x are infinitely small, the graph is increasing. So, this option is false.
D. When x are infinitely small, the graph is decreasing and when x are infinitely large, the graph is increasing. Thus, this option is true.
Answer: correct choice is D.
