Check Whether Every Input Has One Output
Repeated outputs are permitted in a function, but a repeated input cannot be paired with two different outputs.
About 20 minutes, plus any extended practice
Open lesson 1Functions, Nonlinear Patterns, and Domains
A function assigns one output to each allowed input. A table can reveal nonlinear structure or interval-average change, while the domain records which inputs make sense mathematically and in the supplied context.
Before you begin
- Read ordered pairs; calculate differences and squares; distinguish whole-number counts from continuous measurements.
Choose by skill rather than age alone. Read with an adult when useful, revisit a lesson, or explore another grade.
Follow the lesson sequence
Match Squared Inputs to a Table
A quadratic table can arise by multiplying squared inputs by a constant.
About 20 minutes, plus any extended practice
Open lesson 2Calculate Average Change across an Interval
Average rate of change measures the net output change per net input change between two endpoints.
About 20 minutes, plus any extended practice
Open lesson 3Restrict a Function to Meaningful Counts
A counting context supplies input restrictions beyond a formula.
About 20 minutes, plus any extended practice
Open lesson 4Review and transfer
After the lessons, try 4 new review cases and a practical task. Each answer has an explanation and a link back to the related lesson.
Open the unit reviewGuest answers are temporary. Keep your own paper or document; this unit does not certify completion or record a school grade.
Topic references
- California CCSS mathematics topic reference: topic reference — Functions, Nonlinear Patterns, and Domains
These references informed the topic selection. They do not certify complete standards alignment.