"In mathematics, you don't understand things; you just get used to them." John von Neumann
Precalculus Course Outline
Functions
This section introduces the concept of functions, including function notation and evaluating functions.
A diagram showing a function, such as f(x) = x^2, graphed on a Cartesian plane. Mathematics Libre Texts
Linear Functions
Explore linear functions, including slope, intercepts, and graphing linear equations.
Visuals illustrating the concept of slope and y-intercept, along with the graph of a linear equation, such as y = mx + b. School Tube
Systems of Linear Functions
Learn about systems of linear equations and how to solve them using various methods such as substitution and elimination.
An illustration of two linear functions graphed on the same plane showing their point of intersection. Open Textbook
Power and Polynomial Functions
Study power functions and polynomial functions, including their properties and graphing techniques.
Graphs of various polynomial functions, demonstrating different shapes depending on the degree of the polynomial. Lumen Learning
Rational Functions
Examine rational functions and their characteristics, including asymptotes and solving rational equations.
Graphs illustrating the asymptotic behavior of rational functions. Lumen Learning
Modeling Using Variation
Understand the concept of variation and its applications in mathematical modeling.
Diagrams showing direct, inverse, joint, or combined variation in real-world contexts. Slide Player
Exponential Functions
Explore exponential functions, exponential growth and decay, and logarithmic properties.
A graph of an exponential function, showing the characteristic rapid growth or decay. Study.com
Logarithmic Functions
Learn about logarithmic functions, logarithmic properties, and solving logarithmic equations.
The graph of a logarithmic function, showing its characteristic shape. Lumen Learning
Exponential and Logarithmic Equations and Models
Apply exponential and logarithmic functions to solve equations and model real-life situations.
Graphs depicting real-life situations that can be modeled with exponential or logarithmic functions, such as population growth or radioactive decay. Lumen Learning
Evaluating Trigonometric Functions
Introduce trigonometric functions, including sine, cosine, and tangent, and learn to evaluate them.
The unit circle diagram showing sine, cosine, and tangent values for different angles. Matter of Math
Graphing Trigonometric Functions
Study the graphs of trigonometric functions and their transformations.
Graphs of sine, cosine, and tangent functions. Owlcation
Trigonometric Identities
Explore trigonometric identities, including Pythagorean identities and sum and difference identities.
Diagrams or proofs demonstrating trigonometric identities, such as those involving Pythagorean identities. Steve Stein
Inverse Trigonometric Functions and Solving Trigonometric Equations
Understand inverse trigonometric functions and their properties, as well as solving trigonometric equations.
Graphs of inverse trigonometric functions and illustrations of how they can be used to solve trigonometric equations. OnlineMathLearning.com
Further Applications of Trigonometry
Apply trigonometric functions to solve real-world problems and explore additional trigonometric concepts.
Diagrams showing real-world applications of trigonometry, such as navigation and physics problems. Trigonometric Identities
Analytic Geometry
Learn about analytic geometry, including distance and midpoint formulas, and equations of circles and conics.
Graphs and diagrams illustrating the principles of analytic geometry, such as the equation of a circle or elipse. Cue Math
Sequences, Series, and the Binomial Theorem
Study sequences, series, and the binomial theorem, including arithmetic and geometric sequences, and binomial expansions.
Diagrams or sequences demonstrating arithmetic and geometric sequences, as well as the expansion of binomials. HotCore
