Precalculus
Chapter 2
Polynomial, Power, and Rational Functions
Section 1: Linear and Quadratic Functions and Modeling (pages 170 – 187)
Objective: Students will be able to recognize and graph linear and quadratic functions,
and use these functions to model situations and solve problems.
Self Assessment Exercises: # 3, 7, 21, 31, 33, 40, 49, 55, 61, & 63.
Section 2: Power Functions with Modeling (pages 188 – 199)
Objective: Students will be able to sketch power functions in the form of f(x) = k xa
(where k and a are rational numbers).
Self Assessment Exercises: #3, 10, 13, 17, 27, 33, 43, 55, 57, & 66.
Section 3: Polynomial Functions of Higher Degree with Modeling (pages 200 – 213)
Objective: Students will be able to graph polynomial functions, predict their end
behavior, and find their real zeros using a grapher or an algebraic method.
Self Assessment Exercises: # 3, 7, 15, 19, 33, 36, 41, 59, 61, 63, 67, & 75.
Section 4: Real Zeros of Polynomial Functions (pages 214 – 227)
Objective: Students will be able to divide polynomials using long division or synthetic
division; to apply the Remainder Theorem, Factor Theorem, and Rational Zeros
Theorem; and find upper and lower bounds for zeros of polynomials.
Self Assessment Exercises: #3, 7, 15, 19, 27, 33, 35, 37, 49, 55, 62, & 71.
Section 5: Complex Zeros and the Fundamental Theorem of Algebra (pages 228 –
236)
Objective: Students will be able to factor polynomials with real coefficients using factors
with complex coefficients.
Self Assessment Exercises: #3, 7, 15, 29, 33, 37, 42, & 44.
Section 6: Graphs of Rational Functions (pages 237 – 247)
Objective: Students will be able to describe the graphs of rational functions, identify
horizontal and vertical asymptotes, and predict the end behavior of rational functions.
Self Assessment Exercises: #1, 9, 19, 29, 39, 41, 44, 47, 55, & 72.
Section 7: Solving Equations in One Variable (pages 248 – 256)
Objective: Students will be able to solve equations involving fractions using both
algebraic and graphical techniques and identify extraneous solutions.
Self Assessment Exercises: #3, 7, 13, 17, 31, 35, 37, & 39.
Precalculus
Chapter 2
Polynomial, Power, and Rational Functions
Section 8: Solving Equations in Two Variables (pages 257 – 267)
Objective: Students will be able to solve inequalities involving polynomials and rational
functions by using both algebraic and graphical techniques.
Self Assessment Exercises: #1, 11, 15, 21, 25, 43, 49, 53, 54, 59, & 61.
Chapter Test: Key Ideas to Know for the Test
Properties, Theorems, and Formulas
Properties of the Correlation Coefficient (174)
Vertex Form of a Quadratic Function (178)
Vertical Free-Fall Motion (180)
Theorem Local Extrema and Zeros of Polynomial Functions (202)
Leading Term Test for Polynomial End Behavior ((204)
Zeros of Odd/Even Multiplicity (206)
Intermediate Value Theorem (206)
Division Algorithm for Polynomials (214)
Remainder Theorem (215)
Factor Theorem (216)
Rational Zeros Theorem (219)
Fundamental Theorem of Algebra (228)
Linear Factorization Theorem (228)
Complex Conjugate Zeros Theorem (230)
Factors of a Polynomial with Real Coefficients (232)
Polynomial Function of Odd Degree (233)
Graph of a Rational Function (240)
Procedures
Regression Analysis (176)
Polynomial Long Division (214)
Synthetic Division (218)
Solving Inequalities Using Sign Charts (257)
Chapter Project: page 273.