MAT205-0802A-03 College Math - Phase 3 Discussion Board - Essay Example

Polynomial Functions According to Elizabeth Stapel (Polynomials: Definitions Evaluation, 2008), polynomials are sums of expressions consisting ofexpressions. These expressions are called “terms” which are composed of variables, constants, coefficients and/or exponents. The exponents must be whole numbers and variables only.The behaviour of a spring in motion is best described by the elastic potential energy equation. As the spring is pulled away from its base a potential energy is formed in the equation presented below (Equation 1).

This equation is a polynomial with a leading term kx2 , where k is the constant of elasticity and x pertaining to the distance of pull. (Freedman & Young, 1996)Equation 1. Equation for Elastic Potential EnergyFigure 1. Graph of Elastic Potential Energy WThe data above was generated from Equation 1 with the k=4 and x being considered as a unit of distance for simplicity. A trend line of polynomial provides the best fit equation. The bouncing behaviour of the spring is illustrated by the parabolic shape of the potential energy.

As x approaches zero (as the spring shrinks back to its original form) the potential energy becomes zero and is converted to a fully kinetic energy.Rational Functions Rational functions are the result of finding the quotient between two polynomial functions. (Zobel, 2008) It can be symbolized using this general equation:Wherein s(x) and t(x) are polynomial functions and t(x) is not equal to zero.An example of a rational function is illustrated on Equation 3:Equation 2. Example Rational Function  Figure 2.

Graph of a Rational Function Due to the asymptote at x=2, there is a discontinuity. The function approaches infinity at this point. BibliographyFreedman, R., & Young, H. (1996). University Physics. Sta. Barbara: Addison Wesley.Stapel, E. (2008). Polynomials: Definitions / Evaluation. Retrieved April 26, 2008, from Purplemath: http://www.purplemath.com/modules/polydefs.htmZobel, E. A. (2008). Definition of a Rational Function. Retrieved April 26, 2008, from Zona Land: Education in Physics and Mathematics: http://id.mind.net/~zona/mmts/functionInstitute/rationalFunctions/definition/definition.html