Unit 1: Review and Foundations of Functions
Functions and relations
Domain and range
Function notation and evaluation
Vertical line test
Piecewise-defined functions

Transformations of functions
Translations, reflections, stretches and compressions
Parent functions

Operations on functions
Sum, difference, product, quotient
Composition of functions
Inverse functions
Linear equations and inequalities Solving multi-step equations Absolute value equations and inequalities Compound inequalities

Systems of equations Solving by graphing, substitution, elimination Systems with three variables Systems of inequalities and linear programming
Matrices (in some courses) Matrix operations Determinants and inverses Solving systems with matrices
Graphing quadratics
Standard, vertex, and factored forms
Vertex, axis of symmetry, intercepts

Solving quadratics
Factoring
Square roots and completing the square
Quadratic formula and the discriminant

Complex numbers
Imaginary unit i
Operations with complex numbers
Complex solutions of quadratics

Quadratic inequalities
Systems with quadratics (linear-quadratic, quadratic-quadratic)
Polynomial basics
Degree, leading coefficient, end behavior
Adding, subtracting, multiplying polynomials

Polynomial division
Long division
Synthetic division

Zeros and factors
Remainder and Factor TheoremsRational Root Theorem
Fundamental Theorem of Algebra
Complex conjugate root theorem

Graphing polynomials
Multiplicity of zerosTurning points

Solving polynomial equations and inequalities

Polynomial identities (sum/difference of cubes, binomial theorem, Pascal’s triangle)
Radical expressions and functions
nth roots and rational exponents
Simplifying and operating with radicals
Graphing radical functions
Solving radical equations and extraneous solutions

Rational expressions and functions
Simplifying, multiplying, dividing, adding, subtracting
Complex fractions
Graphing rational functions (asymptotes, holes, intercepts)
Solving rational equations and inequalities

Variation
Direct, inverse, joint, and combined variation
Exponential functions
Growth and decay
Compound interest and the number e
Graphing and transformations

Logarithmic functions
Definition and relationship to exponentials
Graphing logarithmsProperties (product, quotient, power rules)Change of base formula

Solving equations
Exponential equations
Logarithmic equations

Modeling
Half-life, population growth, Newton’s law of cooling
Sequences
Arithmetic sequences (explicit and recursive)
Geometric sequences (explicit and recursive)

Series
Arithmetic series and sigma notation
Finite geometric seriesInfinite geometric series and convergence

Applications (loans, annuities, patterns)
Right triangle trigonometry (review)

Unit circle
Radian and degree measure
Trig values of special angles
Arc length and sector area

Trigonometric functions
Sine, cosine, tangent graphs
Amplitude, period, phase shift, vertical shift
Modeling periodic phenomena

Trigonometric identities
Pythagorean identities
Basic proving of identities

Law of Sines and Law of Cosines (in some courses)Inverse trig functions (in some courses)
Circles (equation, center, radius)
Parabolas (focus, directrix)
Ellipses (foci, major/minor axes)
Hyperbolas (asymptotes, foci)
Data analysis
Measures of center and spread
Standard deviation
Normal distribution and z-scores

Study design
Samples, surveys, experiments, observational studies
Margin of error

Probability
Conditional probability and independence
Permutations and combinations
Binomial distribution

Data modeling
Regression (linear, quadratic, exponential)
Residuals and best-fit models