High School PreCalculus Notes

These notes are from an entire year of high school pre-calculus. They cover topics from the beginning of the year such as functions to content at the end of the year such as complex numbers and vectors. Some topics covered are: Function notation and evaluation Domain and range Transformations of functions (translations, stretches, reflections) Composite functions and inverse functions Trigonometric functions (sine, cosine, tangent, etc.) Trigonometric identities and equations Trigonometric graphs and transformations Applications of trigonometry (e.g., solving triangles, vectors) Polynomial functions (degree, roots, factoring) Rational functions and asymptotes Exponential functions (growth and decay) Logarithmic functions and properties Exponential and logarithmic equations Applications (e.g., exponential growth models, compound interest) Distance and midpoint formulas Slopes of lines and equations of lines (including parallel and perpendicular lines) Conic sections (circles, ellipses, hyperbolas, and parabolas) Polar coordinates and equations Arithmetic sequences and series Geometric sequences and series Summation notation (sigma notation) Applications (e.g., compound interest, annuities) Vector operations (addition, subtraction) Applications of vectors (e.g., displacement, force) Matrix operations (addition, subtraction, multiplication) Understanding limits and their properties Evaluating limits algebraically and graphically Continuity of functions