Algebra Basics

Algebra

Definitions

• Algebra: a branch of mathematics that deals with variables and their relationships, often expressed through the use of symbols, equations, and functions.
• Variable: a symbol that represents a value that can change or vary.
• Constant: a value that does not change or vary.

Key Concepts

• Expressions: a group of numbers, variables, and operations combined using mathematical operations (+, -, x, /).
• Equations: a statement that says two expressions are equal (e.g., 2x + 3 = 5).
• Inequalities: a statement that says one expression is greater than, less than, or equal to another (e.g., 2x + 3 > 5).

Solving Equations and Inequalities

• Linear Equations: equations in which the highest power of the variable is 1 (e.g., 2x + 3 = 5).
• Quadratic Equations: equations in which the highest power of the variable is 2 (e.g., x^2 + 4x + 4 = 0).
• Methods for Solving:
  • Substitution
  • Elimination
  • Graphing
  • Factoring

Functions

• Domain: the set of input values for which a function is defined.
• Range: the set of output values of a function.
• Types of Functions:
  • Linear Functions: f(x) = mx + b
  • Quadratic Functions: f(x) = ax^2 + bx + c
  • Exponential Functions: f(x) = a^x

Graphing

• Coordinate Plane: a graph with two perpendicular number lines (x-axis and y-axis).
• Graph of a Function: a visual representation of a function on the coordinate plane.
• Graphing Methods:
  • Table of Values
  • Point-Plotting
  • Intercepts

Algebra Basics

• Algebra is a branch of mathematics that deals with variables and their relationships, often expressed through symbols, equations, and functions.
• A variable is a symbol that represents a value that can change or vary.
• A constant is a value that does not change or vary.

Expressions, Equations, and Inequalities

• An expression is a group of numbers, variables, and operations combined using mathematical operations (+, -, x, /).
• An equation is a statement that says two expressions are equal (e.g., 2x + 3 = 5).
• An inequality is a statement that says one expression is greater than, less than, or equal to another (e.g., 2x + 3 > 5).

Solving Equations and Inequalities

• Linear equations are equations in which the highest power of the variable is 1 (e.g., 2x + 3 = 5).
• Quadratic equations are equations in which the highest power of the variable is 2 (e.g., x^2 + 4x + 4 = 0).
• Methods for solving equations include substitution, elimination, graphing, and factoring.

Functions

• The domain of a function is the set of input values for which a function is defined.
• The range of a function is the set of output values of a function.
• Types of functions include linear functions (f(x) = mx + b), quadratic functions (f(x) = ax^2 + bx + c), and exponential functions (f(x) = a^x).

Graphing

• A coordinate plane is a graph with two perpendicular number lines (x-axis and y-axis).
• The graph of a function is a visual representation of a function on the coordinate plane.
• Graphing methods include the table of values, point-plotting, and intercepts.