Recognize characteristics of graphs of polynomial functions
Polynomial functions of degree 2 or more have graphs that do not have sharp corners; recall that these types of graphs are called smooth curves. Polynomial functions also display graphs that have no breaks. Curves with no breaks are called continuous. Figure 1 shows a graph that represents a polynomial function and a graph that represents a function that is not a polynomial.
![Graph of f(x)=x^3-0.01x.](https://courses.lumenlearning.com/vccs-mth163-17sp/wp-content/uploads/sites/1621/2015/06/CNX_Precalc_Figure_03_04_0012.jpg)
Example 1: Recognizing Polynomial Functions
Which of the graphs in Figure 2 represents a polynomial function?![Two graphs in which one has a polynomial function and the other has a function closely resembling a polynomial but is not.](https://courses.lumenlearning.com/vccs-mth163-17sp/wp-content/uploads/sites/1621/2015/06/CNX_Precalc_Figure_03_04_0022.jpg)
Solution
The graphs of f and h are graphs of polynomial functions. They are smooth and continuous.
The graphs of g and k are graphs of functions that are not polynomials. The graph of function g has a sharp corner. The graph of function k is not continuous.
Q & A
Do all polynomial functions have as their domain all real numbers?
Yes. Any real number is a valid input for a polynomial function.