Algebra Tags

Algebra 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
  • 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
  • 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
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