Relations, Domain, and Range
I can name the domain and range of a relation and decide whether it is a function.
What students learn
Students learn to write the domain and range of a relation as sets and decide whether it is a function by checking each input.
See inside
The key rule
Write each set in braces, each value once, smallest first. A relation is a function when no input has two different outputs.
{1, 2, 3}: no repeats, in order
A y-value may repeat: (1, 5) and (2, 5) can both be in a function.
Watch out
Is (1, 6), (2, 6), (3, 6) a function?
The mistake: no: the output 6 repeatsThe test never looks at repeated outputs.
The fix: each input has one output: yes, it is a functionOnly one input with two outputs would break it.
The mistakes it targets
- Rules out a function because an output repeats
- Swaps the domain and the range
- Lists a repeated value twice in a set
- Calls a relation a function when one input has two outputs
The interactive Teacher Deck (32 slides, PowerPoint)
- The Learn page taught on screen: 8 fill-in blanks, each filled on its own click as students write it
- The worked example one slide per step (four steps), each with the reason for the step
- Six practice and three apply problems: a your-turn slide with a think-time bar, then the solution one line per click
- Jump buttons on every slide: go straight to any problem, the answer bank or the exit ticket
- Speaker notes on each problem: the question to ask, the worked answer and the common error to listen for
- A completed deck PDF (19 pages) with every slide fully built, to print or post
The student packet (9 pages)
- Learn: guided notes with four definitions, the key rule, a worked example and a Watch Out error pair
- Practice: two warm-up, two standard and two stretch problems, with an answer bank for self-checking that hides three common-mistake decoys
- Apply: one word problem, a reasoning prompt and one error analysis
- Assess: an exit ticket of four items, two per page, with an I-can self-rating
- Homework (page 5): eight new problems, two warm-up, four standard and two stretch
- Answer key (pages 6–7): every problem worked step by step, four common mistakes with what to do about each, and a grading guide, plus the homework key (page 8)
- Color and ink-saver editions of the whole packet
Standard codes refer to the Common Core State Standards for Mathematics. Math Class 678 is an independent publisher, not affiliated with, sponsored by, or endorsed by NGA Center or CCSSO. Every product is sold on Teachers Pay Teachers.