Worksheets · Precalculus

Interval notation worksheet for Precalculus

Precalculus writes almost every domain, range and solution set in interval notation, so it needs to be automatic. The harder cases are unions, where an "or" becomes the symbol ∪, and sets read off a number line with open and closed dots.

Also taught in Algebra 2, 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

Interval Notation

Date Period

Write each in interval notation.

  1. Write in interval notation

    Write in interval notation: x<1
  2. Write in interval notation: x≤15
  3. Write in interval notation: x<−4 or x>8
  4. Write in interval notation: −14<x<−1
  5. Write in interval notation: x>13
  6. Write in interval notation: x>−5
  7. Write in interval notation: x<−12
  8. Write in interval notation: x≥−13
  9. Write in interval notation: x≤−4
  10. Write in interval notation: x<6 or x>16

  1. Write the graph in interval notation

    Write the graph in interval notation.-5-4-3-2-1012
  2. Write the graph in interval notation.01234567891011
  3. Write the graph in interval notation.-7-6-5-4-3-2-10
  4. Write the graph in interval notation.-8-7-6-5-4-3-2-10123
  5. Write the graph in interval notation.-1012345
  6. Write the graph in interval notation.-4-3-2-10123
  7. Write the graph in interval notation.-7-6-5-4-3-2-1
  8. Write the graph in interval notation.-3-2-1012345
  9. Write the graph in interval notation.-9-8-7-6-5-4-3-2-1012
  10. Write the graph in interval notation.-5-4-3-2-1012

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

Sigma Prep · sigmaprep.io/worksheets

Name

Interval NotationAnswer keyVersion 2

Date Period

Write each in interval notation.

  1. Write in interval notation

    Write in interval notation: x<1(−∞,1)
  2. Write in interval notation: x≤15(−∞,15]
  3. Write in interval notation: x<−4 or x>8(−∞,−4)∪(8,∞)
  4. Write in interval notation: −14<x<−1(−14,−1)
  5. Write in interval notation: x>13(13,∞)
  6. Write in interval notation: x>−5(−5,∞)
  7. Write in interval notation: x<−12(−∞,−12)
  8. Write in interval notation: x≥−13[−13,∞)
  9. Write in interval notation: x≤−4(−∞,−4]
  10. Write in interval notation: x<6 or x>16(−∞,6)∪(16,∞)

  1. Write the graph in interval notation

    Write the graph in interval notation.-5-4-3-2-1012(−∞,−3]∪(0,∞)
  2. Write the graph in interval notation.01234567891011(3,8]
  3. Write the graph in interval notation.-7-6-5-4-3-2-10(−∞,−5]∪[−2,∞)
  4. Write the graph in interval notation.-8-7-6-5-4-3-2-10123(−5,0)
  5. Write the graph in interval notation.-1012345[1,3)
  6. Write the graph in interval notation.-4-3-2-10123(−∞,−2)∪(1,∞)
  7. Write the graph in interval notation.-7-6-5-4-3-2-1[−5,−3]
  8. Write the graph in interval notation.-3-2-1012345(−∞,−1)∪[3,∞)
  9. Write the graph in interval notation.-9-8-7-6-5-4-3-2-1012[−6,−1)
  10. Write the graph in interval notation.-5-4-3-2-1012(−∞,−3)∪[0,∞)

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

How to do these

Write in interval notation: x≤−4 or x>2

  1. x ≤ -4 runs from negative infinity up to -4, included: (-∞, -4].
  2. x > 2 runs from 2, not included, to infinity: (2, ∞).
  3. Or joins them with a union.

The answer is (−∞,−4]∪(2,∞).

Where students go wrong

Writing the two pieces as one interval. (-4, 2) is the gap between them, the exact opposite set; an "or" with two rays always needs the union symbol.

Also called writing intervals, set notation or parenthesis and parenthesis notation.

What you can put on this worksheet

An inequality as an interval
Write in interval notation: x≤−5 → (−∞,−5]
Read an interval off a number line
Write the graph in interval notation. — number line, labeled -1, 0, 1, 2, 3 → (−∞,1)

Questions about these worksheets

Yes. Every interval notation 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.

Precalculus is usually taken around 11th or 12th 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 interval notation 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 2: an inequality as an interval and read an interval off a number line. Tick as many as you want and set how many of each, or let it spread them evenly.

Using a square parenthesis against infinity. It is never included, so it always takes a round one. The other slip is reversing the order: the smaller number always comes first.