Precalculus Tags

# Precalculus Tags

## Algebra of real numbers and simplifying expressions

- Properties
- Algebraic expressions
- Evaluating expressions
- Inequalities and intervals
- Simplifying expressions
- Solving linear equations in one variable
- Isolating variables
- Solving algebraic equations
- Scientific notation

## Absolute value expressions and functions

## Exponents, rational exponents and radicals

## Cartesian coordinate system

- Plotting points
- Midpoint and distance formulas
- Circles
- Graphs of equations

## Factoring

## Functions

- Definition, concept
- Function notation
- Graphs
- Domain and range
- Piecewise functions
- Compositions and combinations of functions
- Difference quotient

## Transformations of functions and graphs

- Shifts: vertical and horizontal
- Scale changes: vertical and horizontal
- Shift and scale change
- Reflect
- Reflect and shift
- Reflect and scale change
- Symmetry: even, odd, neither
- Three or more transformations
- Vertical shifts
- Horizontal shifts
- Vertical stretches and compressions
- Horizontal stretches and compressions
- Reflections and symmetry
- Graphs

## Linear equations and functions

- Finding the slope
- Parallel and perpendicular lines
- Equations of lines: slope-intercept form
- Equations of lines: point-slope form
- Equations of lines: standard form
- Equations of lines: general
- Linear functions
- Linear equations
- Linear inequalities
- Graphs of lines

## Quadratic equations and functions

- Solve by factoring
- Completing the square
- Quadratic formula
- Complex roots
- Solving equations
- Forms: vertex, factored, general
- Inequalities
- Graphs

## Operations on polynomial and rational expressions

- Polynomials: add, subtract
- Polynomials: multiply
- Polynomials: divide
- Rational expressions: multiply, divide
- Rational expressions: add, subtract
- Simplify rational expressions
- Partial fractions

## Polynomial equations and functions

- Polynomial equations
- Polynomial functions
- Inequalities involving polynomials
- Remainder and factor theorems
- Zeros and multiplicities
- Counting zeros
- Graphs of polynomials
- Complex roots

## Variation and power functions

- Direct variation
- Inverse variation
- Mixed variation
- Power functions

## Systems of equations and inequalities

- Linear systems
- Nonlinear systems
- Inequalities

## Functions with fractional exponents and radical functions

## Rational equations and functions

- Simplifying
- Rational equations
- Rational functions
- Rational inequalities
- Graphs of rational functions
- Asymptotes

## Inverse functions

- One-to-one functions
- Finding the inverse function

## Exponential and logarithmic expressions and functions

- Exponential functions
- Logarithmic functions
- Hyperbolic functions
- Exponential and logarithmic equations
- Inequalities
- Graphs

## Finite sequences and series

- Notation
- Arithmetic
- Binomial theorem
- Summation formulas

## Conic sections

- Parabolas
- Circles
- Ellipses
- Hyperbolas
- Intersections of conics
- Polar or parametric form

## Geometric and algebraic foundations for trigonometry

- Similar figures
- The Pythagorean theorem & its converse
- Radians, converting radians & degrees
- Arc length, sector area, angular and linear velocity
- Reference angles (using coterminal angles)

## Trigonometric functions

- Unit circle
- Sine & cosine functions
- Tangent & cotangent functions
- Secant & cosecant functions
- Inverse trigonometric functions
- Combinations and compositions of functions
- Trigonometric functions of special angles
- Trigonometric functions of non-special angles

## Triangle trigonometry

- Sine, cosine, and tangent of an angle in a right triangle
- Law of sines
- Law of cosines
- Area of a triangle

## Analytic trigonometry

- Double-angle & half-angle formulas
- Addition & subtraction formulas
- Solving trigonometric equations exactly
- Solving trigonometric equations numerically
- Solving trigonometric inequalities exactly
- Solving trigonometric inequalities numerically
- Product-to-sum & sum-to-product formulas

## Polar coordinates & vectors

- Polar and rectangular coordinates
- Curves
- Inequalities