Worksheets · Algebra 2

Vertical line test worksheet for Algebra 2

Algebra 2 uses the vertical line test as a quick check before domain, range and inverses. Half the questions show a graph: if any vertical line crosses it more than once, it is not a function. The other half show a mapping diagram: if any x has two arrows, it is not a function.

Also taught in Algebra 1, at its own level and with its own examples.

Select your difficulty

Pick more than one for a sheet that mixes them.

The preview can look cramped on a phone. The PDF and printed sheet come out normal.

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

Sigma Prep · sigmaprep.io/worksheets

Name

The Vertical Line Test

Date Period

Decide whether each relation is a function.

  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?−10−10−5−5551010
  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?−10−10−5−5551010
  6. Does this graph show y as a function of x?−10−10−5−5510105
  7. Does this graph show y as a function of x?−10−10−5−5551010
  8. Does this graph show y as a function of x?−10−10−5−5551010
  9. Does this graph show y as a function of x?−10−10−5−5510105
  10. Does this graph show y as a function of x?−10−10−5−5551010

  1. Decide if a mapping shows a function

    Tell whether this relation is a function.xy−5−16−3028
  2. Is this relation a function?xy−3149−5023
  3. Decide whether the mapping shows a function. If it does not, name an input that breaks the rule.xy−5−13234
  4. Does this mapping diagram show a function?xy−5−207−5−167
  5. Does each input in the diagram have exactly one output? Is the relation a function?xy−6−417−4−25912
  6. Is y a function of x in this mapping diagram?xy−4−39789
  7. Is y a function of x in this mapping diagram?xy−6−4−27−5−479
  8. Tell whether this relation is a function.xy−509−6−508
  9. Is this relation a function?xy−2−152711
  10. Does this mapping diagram show a function?xy−4038−6−4−326

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

Sigma Prep · sigmaprep.io/worksheets

Name

The Vertical Line TestAnswer keyVersion 2

Date Period

Decide whether each relation is a function.

  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?−10−10−5−5551010No
  4. Does this graph show y as a function of x?−10−10−5−5551010Yes
  5. Does this graph show y as a function of x?−10−10−5−5551010No
  6. Does this graph show y as a function of x?−10−10−5−5510105Yes
  7. Does this graph show y as a function of x?−10−10−5−5551010No
  8. Does this graph show y as a function of x?−10−10−5−5551010No
  9. Does this graph show y as a function of x?−10−10−5−5510105Yes
  10. Does this graph show y as a function of x?−10−10−5−5551010No

  1. Decide if a mapping shows a function

    Tell whether this relation is a function.xy−5−16−3028No, x=−5 has two arrows
  2. Is this relation a function?xy−3149−5023Yes
  3. Decide whether the mapping shows a function. If it does not, name an input that breaks the rule.xy−5−13234Yes
  4. Does this mapping diagram show a function?xy−5−207−5−167No, x=0 has two arrows
  5. Does each input in the diagram have exactly one output? Is the relation a function?xy−6−417−4−25912No, x=−4 has two arrows
  6. Is y a function of x in this mapping diagram?xy−4−39789Yes
  7. Is y a function of x in this mapping diagram?xy−6−4−27−5−479Yes
  8. Tell whether this relation is a function.xy−509−6−508No, x=9 has two arrows
  9. Is this relation a function?xy−2−152711Yes
  10. Does this mapping diagram show a function?xy−4038−6−4−326No, x=3 has two arrows

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

How to do these

Is this relation a function? A mapping diagram sends −2→4, 0→4, 3→1 and 3→5

  1. Look for an input with more than one arrow: 3 has two.
  2. 3 goes to both 1 and 5.
  3. -2 and 0 sharing the output 4 does not matter.

The answer is No, x=3 has two arrows.

Where students go wrong

Treating two arrows into the same output as a failure. Two inputs can share one output and it is still a function; only one input with two arrows, or a vertical line that crosses the graph twice, breaks it.

Also called vertical line test, is it a function, function or not a function or mapping diagram.

What you can put on this worksheet

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
Is the relation a function
Is this relation a function? {(5,5), (7,2), (5,6), (4,3)} → No: x=5 has two outputs
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
Connected segments
Is this graph a function? → No

Questions about these worksheets

Yes. Every vertical line test 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 2 is usually taken around 10th or 11th 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 vertical line test 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 5: the vertical line test on a graph, a mapping diagram, is the relation a function, tables, graphs and mapping diagrams and connected segments. Tick as many as you want and set how many of each, or let it spread them evenly.

Rejecting two inputs that share an output. That is still a function; only one input with two outputs breaks the rule, which is why a horizontal line passes and a vertical one does not.