Worksheets · Algebra 1

Relations and functions worksheet

A relation is any set of pairs. It is a function when no input is sent to two different outputs: the same x can appear twice only if it comes with the same y. The domain is the set of inputs, the range the set of outputs, each value listed once.

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Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Relations and Functions

Date Period

Answer each question.

  1. Decide if a set of ordered pairs is a function

    Is this relation a function? {(−9,4), (1,−1), (9,9), (1,4), (2,0)}
  2. Is this relation a function? {(−4,6), (3,−5), (−7,6), (0,9), (−5,7)}
  3. Is this relation a function? {(−3,3), (9,−9), (2,5), (0,9), (−9,−9)}
  4. Is this relation a function? {(7,1), (0,−1), (9,−6), (−4,5), (2,−6)}
  5. Is this relation a function? {(2,6), (−9,5), (8,−9), (−9,−9), (3,6)}

  1. Find the domain and range of each relation

    Find the domain and range of the relation in the table. x0−8−25−45y−9−126−42
  2. Find the domain and range of the relation in the table. x−99−34−3−8y−576−5−5−8
  3. Find the domain and range of the relation in the table. x2−2157−2y−5−67−270
  4. Find the domain and range of the relation in the table. x1−70−7−34y7−7−42−12
  5. Find the domain and range of the relation in the table. x5−30−383y−8−5−35−3−1

  1. Use the vertical line test

    Does this graph show y as a function of x?−10−10−5−5551010
  2. Does this graph show y as a function of x?−10−10−5551010−5
  3. Does this graph show y as a function of x?−10−10551010−5−5
  4. Does this graph show y as a function of x?−10−10−5−5551010
  5. Does this graph show y as a function of x?−10−10−551010−55

  1. Decide if a table shows a function

    Is this relation a function? x01−86−8y−4−6−4−4−5
  2. Is this relation a function? x0−24−7−2y9212−6
  3. Is this relation a function? x9−3−872y−352−9−3
  4. Is this relation a function? x−6−5−4−5−2y−65−17−6
  5. Is this relation a function? x3−3−1−25y−8131−8

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Relations and FunctionsAnswer keyVersion 1

Date Period

Answer each question.

  1. Decide if a set of ordered pairs is a function

    Is this relation a function? {(−9,4), (1,−1), (9,9), (1,4), (2,0)}No: x=1 has two outputs
  2. Is this relation a function? {(−4,6), (3,−5), (−7,6), (0,9), (−5,7)}Yes
  3. Is this relation a function? {(−3,3), (9,−9), (2,5), (0,9), (−9,−9)}Yes
  4. Is this relation a function? {(7,1), (0,−1), (9,−6), (−4,5), (2,−6)}Yes
  5. Is this relation a function? {(2,6), (−9,5), (8,−9), (−9,−9), (3,6)}No: x=−9 has two outputs

  1. Find the domain and range of each relation

    Find the domain and range of the relation in the table. x0−8−25−45y−9−126−42D={−8,−4,−2,0,5}, R={−9,−4,−1,2,6}
  2. Find the domain and range of the relation in the table. x−99−34−3−8y−576−5−5−8D={−9,−8,−3,4,9}, R={−8,−5,6,7}
  3. Find the domain and range of the relation in the table. x2−2157−2y−5−67−270D={−2,1,2,5,7}, R={−6,−5,−2,0,7}
  4. Find the domain and range of the relation in the table. x1−70−7−34y7−7−42−12D={−7,−3,0,1,4}, R={−7,−4,−1,2,7}
  5. Find the domain and range of the relation in the table. x5−30−383y−8−5−35−3−1D={−3,0,3,5,8}, R={−8, −5, −3, −1, 5}

  1. Use the vertical line test

    Does this graph show y as a function of x?−10−10−5−5551010No
  2. Does this graph show y as a function of x?−10−10−5551010−5Yes
  3. Does this graph show y as a function of x?−10−10551010−5−5Yes
  4. Does this graph show y as a function of x?−10−10−5−5551010No
  5. Does this graph show y as a function of x?−10−10−551010−55No

  1. Decide if a table shows a function

    Is this relation a function? x01−86−8y−4−6−4−4−5No: x=−8 has two outputs
  2. Is this relation a function? x0−24−7−2y9212−6No: x=−2 has two outputs
  3. Is this relation a function? x9−3−872y−352−9−3Yes
  4. Is this relation a function? x−6−5−4−5−2y−65−17−6No: x=−5 has two outputs
  5. Is this relation a function? x3−3−1−25y−8131−8Yes

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

How to do these

Is this relation a function? {(1,4), (2,5), (1,7), (3,5)}

  1. The input 1 appears twice, with 4 and with 7.
  2. One input, two outputs: not a function.

The answer is No, x=1 is sent to two values.

Where students go wrong

Rejecting a relation because an output repeats. Two inputs sharing an output is fine; it is a shared input that breaks it.

Also called ordered pairs or domain and range of a relation.

What you can put on this worksheet

Is the relation a function
Is this relation a function? {(5,5), (7,2), (5,6), (4,3)} → No: x=5 has two outputs
Domain and range of a set of points
Find the domain and range of {(5,5), (7,2), (0,9), (4,3)} → D={0,4,5,7}, R={2,3,5,9}
The range for a given domain
Find the range of f(x)=−3x+1 for the domain {1,2,4} → {−11,−5,−2}
The vertical line test on a graph
Does this graph show y as a function of x? → No
A mapping diagram
Is y a function of x in this mapping diagram? — a mapping diagram with 5 arrows → No, x=2 has two arrows
Discrete or continuous
Is this graph discrete or continuous? → Continuous
Function or not, from a table
Is this relation a function? x628−4y2−225 → Yes
Tables, graphs and mapping diagrams
Graph the relation, and say whether it is a function:
{(−6,0), (1,−4), (7,−2), (5,1), (7,−6), (−6,2)} → Not a function
Points on a grid: pairs, domain, range, function
Record each point as an ordered pair. Then state the domain, the range, and whether each input has only one output. → {(−6,0), (1,3), (5,1), (7,−2)}; D={−6,1,5,7}, R={−2,0,1,3}; Function

Questions about these worksheets

Yes. Every relations and functions sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.

Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.

Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.

Algebra 1 is usually taken around 8th or 9th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.

Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.

That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the relations and functions questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.

Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.

You pick from 9: is the relation a function, domain and range of a set of points, the range for a given domain, the vertical line test on a graph, a mapping diagram, discrete or continuous, function or not, from a table, tables, graphs and mapping diagrams and points on a grid: pairs, domain, range, function. Tick as many as you want and set how many of each, or let it spread them evenly.

Rejecting a relation because an output repeats. Two inputs sharing an output is fine; it is a shared input that breaks it.