How to know if a graph is a polynomial function?
Understand the Problem
The question is asking about the characteristics or criteria that can help identify whether a given graph represents a polynomial function. This involves understanding concepts such as the shape of the graph, continuity, and the presence or absence of curves that suggest polynomial behavior.
Answer
The graph of a polynomial function touches the x-axis at even multiplicities, crosses at odd multiplicities, and is a smooth curve.
The graph of a polynomial function touches the x-axis at zeros with even multiplicities, crosses the x-axis at zeros with odd multiplicities, and is a smooth and continuous curve.
Answer for screen readers
The graph of a polynomial function touches the x-axis at zeros with even multiplicities, crosses the x-axis at zeros with odd multiplicities, and is a smooth and continuous curve.
More Information
Polynomial functions have predictable end behaviors, with the degree and leading coefficient indicating how the graph behaves as x approaches positive or negative infinity.
Tips
Be careful not to confuse polynomial graphs with piecewise or rational functions, as they may have sharp turns or discontinuities, unlike polynomials.
Sources
- Graphs of Polynomial Functions | College Algebra - Lumen Learning - courses.lumenlearning.com
- Graphs of Polynomial Functions - Mathematics LibreTexts - math.libretexts.org
- College Algebra Tutorial 35: Graphs of Polynomial Functions - wtamu.edu
