Functions and graphs: a learning progression
Connect inputs and outputs across equations, tables, and graphs, then study transformations and composition.
Before you begin
Plot coordinates and evaluate algebraic expressions.
Readiness depends on the ideas you can use, not only your age or grade. Start earlier in the sequence when an example feels unfamiliar.
How the skill develops
- Plot ordered pairs and interpret axes and units.
- Recognize functions and distinguish domain from range.
- Read slope and intercepts as features of a relationship.
- Compare families of functions, transformations, inverses, and composition.
What grade is this taught?
Our catalog includes this progression from grade 5 through grade 12. That is a map of the practice available here, not a rule that every school uses the same schedule. Earlier grades may introduce models that later grades formalize.
The sequence is our teaching organization, informed by the published curriculum reference. High-school courses and calculus enrollment vary; check your school’s syllabus for placement decisions.
Build your next practice steps
Mark skills you already feel comfortable with. We’ll suggest the next unchecked skills in this sequence. This is a self-selected path, not a test score.
Grade 8
Grade 9
Grade 11
Common wrong turns along this path
- Treating function notation as multiplication
- Swapping slope and intercept
- Reversing just one subtraction in slope
- Losing restrictions when canceling factors
- Applying functions in the wrong order