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

## 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

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

## Operations on polynomial and rational expressions

• Polynomials: multiply
• Polynomials: divide
• Rational expressions: multiply, divide
• 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
• 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