This course fulfills the Course Objectives for MTH 165 (College Algebra) and MTH 175 (Precalculus) at Monroe Community College, Rochester NY
- Review of sets of numbers, properties of real numbers, order of operations, factoring, and simplifying expressions involving exponents, radicals, or rational expressions. Solve linear equations and inequalities.
- Chapter 1. Methods of solving equations. Solve by factoring, square root property, complete the square and the quadratic formula. Solve rational equations, radical equations, equations with rational exponents, and equations quadratic in form. Solve linear absolute value equations and inequalities. Construct and solve variation equations.
- Chapter 2. Attributes of functions found algebraically and graphically. Graphing functions by using transformations. Piecewise functions, combinations or functions, and composition. One-to-one and inverse functions.
- Chapter 3. Quadratic functions and circles: identify attributes and graph. Polynomial functions: Identify end behavior, find zeros, and graph. Polynomial long division and synthetic division. Remainder theorem, factor theorem, rational zero theorem. Solve polynomial and rational inequalities.
- Chapter 4. Exponential and Logarithmic Functions. Properties of exponents, graphs of exponential functions and their transformations. Properties of logarithms, graphs of logarithmic transformations and their graphs. Solve exponential and logarithmic equations using function properties, one-to-one property, writing in alternate form, and taking the log or exponentiating both sides of the equation. Solve application problems: compound interest, exponential growth and decay, logarithmic application
- The trigonometric functions are functions of an angle. and relate the angles of a triangle to the lengths of its sides. They are important in the study of triangles and modeling periodic phenomena, among many other applications.
- In this chapter, we will investigate graphs of sine, cosine, and other trigonometric functions.
- In this chapter, we discuss how to manipulate trigonometric equations algebraically by applying various formulas and trigonometric identities. We will also investigate some of the ways that trigonometric equations are used to model real-life phenomena.
- In this chapter, we will explore applications of trigonometry that will enable us to solve many different kinds of problems, including finding the height of a tree. We extend topics we introduced in Trigonometric Functions and investigate applications more deeply and meaningfully.