Chapter 2 - Polynomial, Power and Rational Functions
"In this chapter and the next two, we will explore the theory and applications of specific families of functions. We begin this exploration by studying three interrelated families of functions: polynomial, power, and rational functions. These three families of functions are used in the social, behavioral, and natural sciences."
"This chapter includes a thorough study of the theory of polynomial equations. We investigate algebraic models for finding both real- and complex-number solutions of such equations and relate these methods to the graphical behavior of polynomial and rational functions. The chapter closes by extending these methods to inequalities in one variable."
(Demana, Franklin D. "Chapter 2." Precalculus: Graphical, Numerical, Algebraic. 7th ed. Boston: Addison-Wesley, 2007. 170. Print.)
Humidity and relative humidity are measures used by weather forecasters. Humidity affects our comfort and our health. If humidity is too low, our skin can become dry and cracked, and viruses can live longer. If humidity is too high, it can make warm temperatures feel even warmer, and mold, fungi, and dust mites can live longer. See page 244 to learn how relative humidity is modeled as a rational function.
Lesson 2.1 - Linear & Quadratic Functions & Modeling
We will cover polynomial functions, linear functions & their graphs, average rate of change, linear correlation and modeling, quadratic functions and their graphs, and applications of quadratic functions.
Lesson 2.2 - Power Functions with Modeling
This lesson covers power functions and variation, monomial functions and their graphs, graphs of power functions, and modeling with power functions.
Lesson 2.3 - Polynomial Functions of Higher Degree with Modeling
This lesson will cover graphs of polynomial functions, the end behavior of polynomial functions, zeros of polynomial functions, the Intermediate Value Theorem, and Modeling.
Lesson 2.4 - Real Zeros of Polynomial Functions
In this lesson students will learn about long and synthetic division, the Remainder, Factor, and Rational Zeros theorems, and Upper and Lower bounds.
Lesson 2.5 - Complex Zeros and the Fundamental Theorem of Algebra
This lesson covers the Fundamental Theorem of Algebra, the Linear Factorization Theorem, Complex Conjugate Zeros, and factoring with real number coefficients. Students will be able to factor polynomials with real coefficients using factors with complex coefficients.
Lesson 2.6 - Graphs of Rational Functions
This lesson covers rational functions, transformations of the reciprocal function, limits and asymptotes, analyzing graphs of rationals functions, and exploring relative humidity.
Lesson 2.7 - Solving Equations in One Variable
In this lesson students will learn how to solve equations involving fractions using both algebraic and graphical techniques and identify extraneous solutions.
Lesson 2.8 - Solving Inequalities in One Variable
In this lesson students will learn how to utilize a sign chart, and how to solve inequalities involving polynomials and rational functions by algebraic and graphical techniques.