Graphs That Are Not Polynomial Functions. Polynomial functions also display graphs that have no breaks. Curves with no breaks are called continuous.
The graphs of f and h are graphs of polynomial functions. If a polynomial contains a factor of the form latex left x h right p latex the behavior near the x intercept h is determined by the power p we say that latex x h latex is a zero of multiplicity p. The graph of function k is not continuous.
The graph of a polynomial function will touch the x axis at zeros with even multiplicities.
Figure 1 shows a graph that represents a polynomial function and a graph that represents a function that is not a polynomial. The graph of function k is not continuous. The graphs of g and k are graphs of functions that are not polynomials. Curves with no breaks are called continuous.
