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

## Cartesian coordinate system

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

## 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
• 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

## 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
• 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