TMCC: Precalculus I and II
- Page ID
- 13383
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This precalculus textmap is intended for college-level Precalculus students and is a comprehensive book that covers more ground than an instructor could likely cover in a typical one- or two-semester course; but instructors should find, almost without fail, that the topics they wish to include in their syllabus are covered in the text.
- 2: Linear Functions
- Recall that a function is a relation that assigns to every element in the domain exactly one element in the range. Linear functions are a specific type of function that can be used to model many real-world applications, such as plant growth over time. In this chapter, we will explore linear functions, their graphs, and how to relate them to data.
- 3: Polynomial and Rational Functions
- In this chapter, we will learn about these concepts and discover how mathematics can be used in such applications.
- 3.0: Prelude to Polynomial and Rational Functions
- 3.1: Complex Numbers
- 3.2: Quadratic Functions
- 3.3: Power Functions and Polynomial Functions
- 3.4: Graphs of Polynomial Functions
- 3.5: Dividing Polynomials
- 3.6: Zeros of Polynomial Functions
- 3.7: Rational Functions
- 3.8: Inverses and Radical Functions
- 3.9: Modeling Using Variation
- 4: Exponential and Logarithmic Functions
- In this chapter, we will explore exponential functions, which can be used for, among other things, modeling growth patterns such as those found in bacteria. We will also investigate logarithmic functions, which are closely related to exponential functions. Both types of functions have numerous real-world applications when it comes to modeling and interpreting data.
- 4.0: Prelude to Exponential and Logarithmic Functions
- 4.1: Exponential Functions
- 4.2: Graphs of Exponential Functions
- 4.3: Logarithmic Functions
- 4.4: Graphs of Logarithmic Functions
- 4.5: Logarithmic Properties
- 4.6: Exponential and Logarithmic Equations
- 4.7: Exponential and Logarithmic Models
- 4.8: Fitting Exponential Models to Data
- 5: Trigonometric Functions
- 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.
- 6: Periodic Functions
- In this chapter, we will investigate graphs of sine, cosine, and other trigonometric functions.
- 7: Trigonometric Identities and Equations
- 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.
- 7.0: Prelude to Trigonometric Identities and Equations
- 7.1: Solving Trigonometric Equations with Identities
- 7.2: Sum and Difference Identities
- 7.3: Double-Angle, Half-Angle, and Reduction Formulas
- 7.4: Sum-to-Product and Product-to-Sum Formulas
- 7.5: Solving Trigonometric Equations
- 7.6: Modeling with Trigonometric Equations
- 7.E: Trigonometric Identities and Equations (Exercises)
- 8: Further Applications of Trigonometry
- 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.
- 8.0: Prelude to Further Applications of Trigonometry
- 8.1: Non-right Triangles: Law of Sines
- 8.2: Non-right Triangles - Law of Cosines
- 8.3: Polar Coordinates
- 8.4: Polar Coordinates - Graphs
- 8.5: Polar Form of Complex Numbers
- 8.6: Parametric Equations
- 8.7: Parametric Equations - Graphs
- 8.8: Vectors
- 8.E: Further Applications of Trigonometry (Exercises)
- 9: Systems of Equations and Inequalities
- In this chapter, we will investigate matrices and their inverses, and various ways to use matrices to solve systems of equations. First, however, we will study systems of equations on their own: linear and nonlinear, and then partial fractions.
- 9.0: Prelude to Systems of Equations and Inequalities
- 9.1: Systems of Linear Equations: Two Variables
- 9.2: Systems of Linear Equations: Three Variables
- 9.3: Systems of Nonlinear Equations and Inequalities - Two Variables
- 9.4: Partial Fractions
- 9.5: Matrices and Matrix Operations
- 9.6: Solving Systems with Gaussian Elimination
- 9.7: Solving Systems with Inverses
- 9.8: Solving Systems with Cramer's Rule
- 9.E: Systems of Equations and Inequalities (Exercises)
- 10: Analytic Geometry
- In this chapter, we will investigate the two-dimensional figures that are formed when a right circular cone is intersected by a plane. We will begin by studying each of three figures created in this manner. We will develop defining equations for each figure and then learn how to use these equations to solve a variety of problems.
- 11: Sequences, Probability and Counting Theory
- In this chapter, we will explore the mathematics behind situations such as these. We will take an in-depth look at annuities. We will also look at the branch of mathematics that would allow us to calculate the number of ways to choose lottery numbers and the probability of winning.
Contributors
Jay Abramson (Arizona State University) with contributing authors. Textbook content produced by OpenStax College is licensed under a Creative Commons Attribution License 4.0 license. Download for free at https://openstax.org/details/books/precalculus.