Podcast
Questions and Answers
What is the branch of mathematics that deals with variables and their relationships?
What is the branch of mathematics that deals with variables and their relationships?
What is a symbol that represents a value that can change or vary?
What is a symbol that represents a value that can change or vary?
What is a statement that says two expressions are equal?
What is a statement that says two expressions are equal?
What type of equation has the highest power of the variable as 1?
What type of equation has the highest power of the variable as 1?
Signup and view all the answers
What is the set of input values for which a function is defined?
What is the set of input values for which a function is defined?
Signup and view all the answers
What type of function has a formula of f(x) = mx + b?
What type of function has a formula of f(x) = mx + b?
Signup and view all the answers
What is a visual representation of a function on the coordinate plane?
What is a visual representation of a function on the coordinate plane?
Signup and view all the answers
What is the graph with two perpendicular number lines (x-axis and y-axis)?
What is the graph with two perpendicular number lines (x-axis and y-axis)?
Signup and view all the answers
What is a method for solving linear equations?
What is a method for solving linear equations?
Signup and view all the answers
Study Notes
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.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Test your understanding of fundamental algebra concepts, including variables, constants, expressions, and equations.
