Domain and Range Graphic Organizer

Domain beside range for ordered pairs, a table, a graph and an equation, with a box for the notation.

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Name:Date:Domain from ordered pairsRange from ordered pairsDomain from a tableRange from a tableDomain from a graphRange from a graphDomain from an equationRange from an equationThe notation I use
Domain and range graphic organizer: four ways to find them Domain beside range in eight boxes: a pair for a list of ordered pairs, for a table, for a graph and for an equation, to write how each is found. The box at the foot is for the notation your class uses.
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How it works

This domain and range graphic organizer sets the two side by side for four ways a relation can be shown. Students write one method in each box, so the page becomes their own reference for the unit.

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Which meaning of range

The word range has two meanings in mathematics: the set of outputs a function actually gives, and the larger set those outputs are allowed to fall in. Newer books generally mean the first, and these sheets do too. Check which one your textbook uses before the boxes are filled in.

Domain and range in the standards

In the Common Core standards for high school, students learn that a function assigns each element of its domain exactly one element of the range, and they relate the domain of a function to its graph and to the situation it describes.

  • Slide a sheet of paper across a graph from left to right: where the graph first and last shows marks the ends of the domain.
  • (2, 5) can be an interval or a point. Have students write which one they mean the first time it appears.

Questions and answers

What is the domain and range of a function?

The domain is the set of inputs the function accepts, which can be thought of as what x can be. The range is the set of outputs the function gives for those inputs.

How do you find the domain and range of a graph?

Read the domain along the x-axis: it is every x-value the graph covers, from left to right. Read the range along the y-axis in the same way, from bottom to top.

How do you write domain and range in interval notation?

Write the two ends of the stretch of numbers with a comma between them. Use a square bracket for an end that is included and a parenthesis for one that is not: −2 ≤ x < 5 becomes [−2, 5).

What values are not in the domain of a function?

For a rule given as a formula, leave out any x the formula cannot be worked out for. 1/x cannot be evaluated at 0, and the square root of x is a real number only when x is 0 or more.

All 14 organizers

Notes charts 5

  • Domain and range graphic organizer: four ways to find them Domain beside range in eight boxes: a pair for a list of ordered pairs, for a table, for a graph and for an equation, to write how each is found. The box at the foot is for the notation your class uses.
  • Notebook half sheets: domain beside range Two half sheets with a cut line between them: a box for each word and a line at the foot for telling them apart.
  • The same as a chart: a row for each source The four sources and the notation printed down the side, with a Domain column beside a Range column.
  • Sideways chart with a box for an example A column for each source on a landscape page: copy or sketch an example at the top, then write its domain and its range under it.
  • Three kinds of graph to sketch A box each for separate points, a piece with two ends and a graph with arrows, to sketch over lines for the domain and range.
Show all 14 organizers (9 more)

Practice 3

  • Domain from an equation: four questions to ask A box for each question, to answer with an equation of your own: a fraction, a square root, a rule with neither, and a rule from a real situation.
  • Exit slips: one relation, two to a page Two half sheets with a cut line between them: one relation, its domain, its range and how you found them.
  • Find the domain and range: eight sets of ordered pairs Eight relations with a box for the domain and a box for the range of each. A value that comes up twice is listed once.

Notation 2

  • Four ways to write it: words, a list, an inequality, an interval A row for each way of writing a domain or a range, with a box for when it is used and a box for an example.
  • Inequality to interval notation: eight to rewrite Eight inequalities to write again as intervals, with a box for which ends are included.

Samples and answer keys 4

  • Answer key: eight sets of ordered pairs The domain and the range of each of the eight relations.
  • Answer key: inequality to interval notation The eight intervals, and which ends each one includes.
  • Sample notation chart, filled in One stretch of numbers written in words, as an inequality and as an interval, with a list for separate values.
  • Sample, filled in: how to find the domain and the range The opening sheet with all nine boxes written in.

How this list was compiled: Our own layouts and wording; no publisher's organizer is copied. What a domain and a range are were checked against the Wikipedia articles Domain of a function and Range of a function, interval notation against the Wikipedia article Interval (mathematics), and the grade wording against the Common Core State Standards for Mathematics, all read October 14, 2026. Both answer keys and both samples were worked out twice. Licence: own work

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