Functions
Supercharge your thinking with the language of algebra.
Seeing Solutions
Graphing Solutions
Revealing Patterns
Choosing Values
Continuity
Using Continuity
Diminishing Returns
Intercepts
Up and Down
Minimums and Maximums
Bounded Graphs
Graphs with Gaps
Apply: Training an AI
Rate of Change
Slope and Parameters
The y-Intercept
Horizontal and Vertical Lines
Linear Systems
Finding How Many Solutions
Apply: Rules of Thumb
What is a Function?
Function Tables
Function Graphs
Domain
Range
Interval Notation
Multiple Intervals
Vertical Shift
Horizontal Shift
Vertical Stretch and Shrink
Horizontal Stretch and Shrink
Vertical Reflections
Horizontal Reflections
Transforming Parabolas
Points on Parabolas
Optimizing Revenue
Solving Quadratics
Factored Form
Factoring a Quadratic
Difference of Squares
Perfect Squares
Completing the Square
General Solution
Solving with the Quadratic Formula
Counting Zeros
Course description
This course explores the twin pillars of algebraic thinking—equations and graphs. With these two tools, we'll unpack algebra's big ideas and develop a powerful perspective to solve its essential problems. By the end of this course, you'll understand graphs and their relationship to the equations they represent, enabling you to answer questions involving equations even when it's impossible to solve them by hand. Though a familiarity with solving equations is helpful, we'll start with a review of the basics and build on them throughout the course. When you finish, you'll be ready to conquer a wide range of algebraic techniques in Algebra 1.
Topics covered
- Algebraic Expressions
- Coordinate Plane
- Equations
- Graphs
- Linear Equations
- Ordered Pairs
- Rates
- Simplifying
- Systems of Equations
- Variables
Prerequisites and next steps
Though a familiarity with solving equations is helpful, we'll start with a review of the basics and build on them throughout the course.