Precalculus

Functions and Their Graphs

Functions: Define functions, identify their domain and range, and evaluate functions.
Graphs of Functions: Graph functions, understand their properties (increasing, decreasing, even, odd), and identify key points.
Library of Basic Functions: Explore common functions such as linear, quadratic, polynomial, rational, exponential, logarithmic, and trigonometric functions.
Graph Transformations: Learn how to transform functions using shifts, stretches, reflections, and compressions.

Linear and Quadratic Functions

Linear Functions and Models: Analyze linear functions, find their equations, and interpret their graphs in real-world contexts.
Quadratic Functions and Models: Explore quadratic functions, graph them, find their vertex, axis of symmetry, and zeros. Solve quadratic equations and inequalities.
Quadratic Equations in the Complex System: Understand complex numbers and solve quadratic equations using the quadratic formula.

Polynomial and Rational Functions

Polynomial Functions and Models: Define polynomial functions, identify their degree and leading coefficient, and graph them.
Zeros of Polynomial Functions: Find zeros of polynomial functions using various methods such as synthetic division, factoring, and the rational root theorem.
Polynomial Division: Divide polynomials using long division and synthetic division.
Rational Functions and Their Graphs: Analyze rational functions, find their vertical, horizontal, and slant asymptotes, and graph them.
Polynomial and Rational Inequalities: Solve polynomial and rational inequalities.

Exponential and Logarithmic Functions

Composition: Understand function composition and find the composition of two functions.
Inverse Functions: Find the inverse of a function and determine if a function has an inverse.
Exponential Functions: Explore exponential functions, their graphs, and their properties.
Logarithmic Functions: Define logarithmic functions as the inverse of exponential functions, understand their properties, and solve logarithmic equations.
Properties of Logarithms: Learn the properties of logarithms, including the product rule, quotient rule, power rule, and change of base formula.
Logarithmic and Exponential Equations: Solve logarithmic and exponential equations.

Trigonometric Functions

Angles and Their Measure: Convert between degrees and radians, find the reference angle, and determine the quadrant of an angle.
Trigonometric Functions via the Unit Circle: Define trigonometric functions using the unit circle, understand their values for special angles, and graph them.
Right Triangle Trigonometry: Apply trigonometric functions to right triangles and solve triangles.
Basic Properties and Graphs of Trigonometric Functions: Explore the properties of trigonometric functions, including period, amplitude, phase shift, and vertical shift, and graph them.

Analytic Trigonometry

Inverse Trigonometric Functions: Define inverse trigonometric functions, find their domain and range, and solve equations involving them.
Trigonometric Equations: Solve trigonometric equations using various techniques, including algebraic methods, factoring, and identities.
Trigonometric Identities: Prove trigonometric identities and use them to simplify expressions and solve equations.

Polar Coordinates

Polar Coordinates: Convert between rectangular and polar coordinates, and graph points in the polar coordinate system.

Polar Equations and Graphs: Graph polar equations and understand their properties.

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