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Function notation
Operations with functions
Adding functions
Subtracting functions
Multiplying functions
Dividing functions
Composite functions
Inequalities of combined functions
Inverse functions
One to one functions
Difference quotient: applications of functions
Transformations of functions: Horizontal translations
Transformations of functions: Vertical translations
Reflection across the y-axis: y = f(-x)
Reflection across the x-axis: y = -f(x)
Transformations of functions: Horizontal stretches
Transformations of functions: Vertical stretches
Combining transformations of functions
Even and odd functions
What is a polynomial function?
Polynomial long division
Polynomial synthetic division
Remainder theorem
Factor theorem
Rational zero theorem
Characteristics of polynomial graphs
Multiplicities of polynomials
Imaginary zeros of polynomials
Determining the equation of a polynomial function
Applications of polynomial functions
Solving polynomial inequalities
Fundamental theorem of algebra
Descartes' rule of signs
Basic radical functions
Transformations of radical functions
Square root of a function
Solving radical equations
What is a rational function?
Point of discontinuity
Vertical asymptote
Horizontal asymptote
Slant asymptote
Graphs of rational functions
Solving rational equations
Solving rational inequalities
Direct variation
Evaluating piecewise functions
Graphing piecewise linear functions
Graphing piecewise non-linear functions
Exponents: Product rule (a^x)(a^y) = a^(x+y)
Exponents: Division rule (a^x / a^y) = a^(x-y)
Exponents: Power rule (a^x)^y = a^(x * y)
Exponents: Negative exponents
Exponents: Zero exponent: a^0 = 1
Exponents: Rational exponents
Solving exponential equations using exponent rules
Graphing exponential functions
Graphing transformations of exponential functions
Finding an exponential function given its graph
What is a logarithm?
Converting from logarithmic form to exponential form
Evaluating logarithms without a calculator
Common logarithms
Natural log: ln
Evaluating logarithms using change-of-base formula
Converting from exponential form to logarithmic form
Solving exponential equations with logarithms
Product rule of logarithms
Quotient rule of logarithms
Combining product rule and quotient rule in logarithms
Evaluating logarithms using logarithm rules
Solving logarithmic equations
Graphing logarithmic functions
Finding a logarithmic function given its graph
Exponential growth and decay by a factor
Exponential decay: Half-life
Exponential growth and decay by percentage
Finance: Compound interest
Continuous growth and decay
Logarithmic scale: Richter scale (earthquake)
Logarithmic scale: pH scale
Logarithmic scale: dB scale
Finance: Future value and present value
Angle in standard position
Coterminal angles
Reference angle
Find the exact value of trigonometric ratios
ASTC rule in trigonometry (All Students Take Calculus)
Unit circle
Converting between degrees and radians
Trigonometric ratios of angles in radians
Radian measure and arc length
Sine graph: y = sin x
Cosine graph: y = cos x
Tangent graph: y = tan x
Cotangent graph: y = cot x
Secant graph: y = sec x
Cosecant graph: y = csc x
Graphing transformations of trigonometric functions
Determining trigonometric functions given their graphs
Ferris wheel trig problems
Tides and water depth trig problems
Spring (simple harmonic motion) trig problems
Quotient identities and reciprocal identities
Pythagorean identities
Sum and difference identities
Cofunction identities
Double-angle identities
Solving first degree trigonometric equations
Determining non-permissible values for trig expressions
Solving second degree trigonometric equations
Solving trigonometric equations involving multiple angles
Solving trigonometric equations using pythagorean identities
Solving trigonometric equations using sum and difference identities
Solving trigonometric equations using double-angle identities
Finding inverse trigonometric function from its graph
Evaluating inverse trigonometric functions
Finding inverse reciprocal trigonometric function from its graph
Finding exact value of inverse reciprocal trig functions
Fundamental counting principle
Factorial notation
Path counting problems
Permutation vs. Combination
Permutations
Combinations
Problems involving both permutations and combinations
Pascal's triangle
Binomial theorem
Conics - Parabola
Conics - Ellipse
Conics - Circle
Conics - Hyperbola
Introduction to imaginary numbers
Complex numbers and complex planes
Adding and subtracting complex numbers
Complex conjugates
Multiplying and dividing complex numbers
Distance and midpoint of complex numbers
Angle and absolute value of complex numbers
Polar form of complex numbers
Operations on complex numbers in polar form
Introduction to vectors
Magnitude of a vector
Direction angle of a vector
Scalar multiplication
Equivalent vectors
Adding and subtracting vectors in component form
Operations on vectors in magnitude and direction form
Unit vector
Word problems on vectors
Notation of matrices
Adding and subtracting matrices
Matrix multiplication
The three types of matrix row operations
Representing a linear system as a matrix
Solving a linear system with matrices using Gaussian elimination
Zero matrix
Identity matrix
Properties of matrix addition
Properties of scalar multiplication
Properties of matrix multiplication
The determinant of a 2 x 2 matrix
The determinant of a 3 x 3 matrix (General & Shortcut Method)
The inverse of a 2 x 2 matrix
The inverse of 3 x 3 matrices with matrix row operations
The inverse of 3 x 3 matrix with determinants and adjugate
2 x 2 invertible matrix
Solving linear systems using Cramer's Rule
Solving linear systems using 2 x 2 inverse matrices
Transforming vectors with matrices
Transforming shapes with matrices
Finding the transformation matrix
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