What type of graph represents a polynomial function?

A polynomial function is represented by a smooth, continuous curve on a graph due to its mathematical properties. Polynomial functions are defined by equations that involve terms with non-negative integer exponents, such as ( ax^n + bx^{n-1} + ... + k ), where ( a, b, ) and ( k ) are constants, and ( n ) is a non-negative integer.

When you graph these functions, the nature of polynomial equations ensures that there are no breaks, holes, or jumps in the curve. This means that as you plot points to represent the values given by a polynomial function for varying inputs, the resulting graph connects these points through a smooth curve, reflecting the continuous nature of these functions over their domain.

In contrast, the other types of graphs mentioned would not depict a polynomial function. Straight lines represent linear functions, disconnected points signify discrete functions, and sets of parallel lines indicate relationships that are linear but do not exhibit polynomial behavior. Therefore, the characteristic of a polynomial graph being a smooth, continuous curve is what makes the correct answer valid.