Functions Contents - A
Prerequisites
The set of real numbers
Rational numbers
Irrational numbers
The real number line, and relations
I
nterval definition and notation
Distance and absolute value
Properties of the real number
s
Properties of exponents
The rules for powers or exponents
Order of operations
Absolute value equations
Linear Inequalities
Absolute value inequalities
Solving linear inequalities with absolute value
Algebraic expressions
Expanding algebraic expression by removing parentheses
The binomial expansion algorithm
Factoring and expanding algebraic expressions, rules for transforming algebraic expressions
Factoring quadratic trinomials
Factoring polynomials
Imaginary and Complex Numbers
Addition and subtraction of complex numbers
Multiplication and division of complex numbers
Polar or trigonometric notation of complex numbers
Multiplication and division of complex numbers in the polar form
Exponentiation and root extraction of complex numbers in the polar form
Powers and roots of complex numbers, use of de Moivre’s formulas
Euler’s formula, relationship between trigonometric functions and the complex exponential function
Linear equation in one variable
Solving linear equations
Linear equation in one variable examples
Linear Inequalities
Solving inequalities
Properties of inequalities
Examples of solving single linear inequalities
Solving compound or double inequalities
Equations with Rational Expressions
Solving rational equations
Rational equations - Linear equations
Rational Inequalities
Method of solving rational inequalities
The graph of the translated equilateral or rectangular hyperbola
Quadratic Equations and Quadratic Function
Quadratic equation
Solving quadratic equations by completing the square,
the quadratic formula
Solving quadratic equations by factoring,
Vieta's formula
Quadratic function or the second-degree polynomial
Vertex
(maximum/minimum) - coordinates of translation
Roots or zeros of the function, axis of symmetry and y-intercept
Transformations of the quadratic function's expression
Graphing a quadratic function
Transformations of the graph of the quadratic function
Binomial equations
Solving binomial equations
Equations reducible to quadratic - biquadratic equations
Solving equations reducible to quadratic
Quadratic inequalities
Solving quadratic inequalities
Graphic solution of quadratic inequalities
Absolute value equations, quadratic equations and functions
Solving quadratic equations with absolute value
Graphing
absolute value functions or equations examples
Radical or irrational equations
Solving irrational or radical equations
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