In Exercises 11–14, identify which graphs are not those of polynomial functions.

Key Concepts

Polynomial Functions

Polynomial functions are mathematical expressions that consist of variables raised to non-negative integer powers, combined using addition, subtraction, and multiplication. They can be represented in the form f(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where a_n, a_(n-1), ..., a_0 are constants and n is a non-negative integer. The graph of a polynomial function is continuous and smooth, without any sharp corners or breaks.

Characteristics of Non-Polynomial Functions

Non-polynomial functions can exhibit various characteristics that distinguish them from polynomial functions. These may include sharp corners, discontinuities, or asymptotic behavior. For example, absolute value functions, piecewise functions, and rational functions can have such features, making their graphs non-smooth or non-continuous at certain points.

Graph Interpretation

Interpreting graphs involves analyzing the visual representation of mathematical functions to identify their properties and behaviors. Key aspects include recognizing shapes, identifying intercepts, and determining continuity or discontinuity. In the context of polynomial functions, a graph that displays sharp turns or breaks indicates that it is not a polynomial, as polynomial graphs are characterized by their smooth curves.