Precalculus: Mathematics for Calculus notes

Explains and has examples for transforming functions, such as quadratics. Horizontal and vertical shrinks and stretches. Horizontal and vertical shifts, reflections, and even and odd functions.

Equations for slope, horizontal lines, and vertical lines. Slope-intercept, point-slope, and linear forms. Connections between parallel and perpendicular lines on a graph.

Gives examples of composite functions and the algebra of functions. How to combine functions using addition, subtraction, multiplication, and division.

Explains standard quadratic form and vertex form and has examples for them. Explains maximums and minimums, and local maximums and minimums.

Simplifying exponents, and fractions with exponents. Rational exponents and radicals. Rationalizing denominators.

Modeling different functions and rules with word problem examples.

Explains functions, domain, range, piecewise functions, and how to find domains. Also gives examples for each of these.

Simplifying rational expressions, compound rational expressions, and rationalizing the numerator of a fraction.

Joint, direct, and inverse variations, equations for all. Examples for all the variations.

Factoring algebraic expressions completely, examples. Getting a special product from a cubed equation.