Worksheets · Algebra 1

Domain of a function worksheet for Algebra 1

Algebra 1 asks which inputs a function allows: a square root needs a non-negative inside, and a fraction cannot divide by zero. Each restriction becomes a short inequality or equation, and the answer goes as an inequality like x ≥ -2 or in interval notation.

Also taught in Algebra 2 and Precalculus, each 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

Domain of a Function

Date Period

State the domain in interval notation.

  1. Find the domain of a square root function

    State the domain of f(x)=3x−3
  2. State the domain of f(x)=4x+2
  3. State the domain of f(x)=x−9
  4. State the domain of f(x)=2x−7
  5. State the domain of f(x)=4x+5
  6. State the domain of f(x)=4x−7
  7. State the domain of f(x)=4x+6
  8. State the domain of f(x)=4x−1
  9. State the domain of f(x)=4x+3
  10. State the domain of f(x)=x+3

  1. Find the domain when the variable is in a denominator

    State the domain of f(x)=5x−5
  2. State the domain of f(x)=1x+2
  3. State the domain of f(x)=−2x
  4. State the domain of f(x)=−6x−4
  5. State the domain of f(x)=−3x+1
  6. State the domain of f(x)=4x+6
  7. State the domain of f(x)=−7x−3
  8. State the domain of f(x)=7x−1
  9. State the domain of f(x)=−6x+3
  10. State the domain of f(x)=−4x+4

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

Sigma Prep · sigmaprep.io/worksheets

Name

Domain of a FunctionAnswer keyVersion 2

Date Period

State the domain in interval notation.

  1. Find the domain of a square root function

    State the domain of f(x)=3x−3[1,∞)
  2. State the domain of f(x)=4x+2[−12,∞)
  3. State the domain of f(x)=x−9[9,∞)
  4. State the domain of f(x)=2x−7[72,∞)
  5. State the domain of f(x)=4x+5[−54,∞)
  6. State the domain of f(x)=4x−7[74,∞)
  7. State the domain of f(x)=4x+6[−32,∞)
  8. State the domain of f(x)=4x−1[14,∞)
  9. State the domain of f(x)=4x+3[−34,∞)
  10. State the domain of f(x)=x+3[−3,∞)

  1. Find the domain when the variable is in a denominator

    State the domain of f(x)=5x−5(−∞,5)∪(5,∞)
  2. State the domain of f(x)=1x+2(−∞,−2)∪(−2,∞)
  3. State the domain of f(x)=−2x(−∞,0)∪(0,∞)
  4. State the domain of f(x)=−6x−4(−∞,4)∪(4,∞)
  5. State the domain of f(x)=−3x+1(−∞,−1)∪(−1,∞)
  6. State the domain of f(x)=4x+6(−∞,−6)∪(−6,∞)
  7. State the domain of f(x)=−7x−3(−∞,3)∪(3,∞)
  8. State the domain of f(x)=7x−1(−∞,1)∪(1,∞)
  9. State the domain of f(x)=−6x+3(−∞,−3)∪(−3,∞)
  10. State the domain of f(x)=−4x+4(−∞,−4)∪(−4,∞)

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

How to do these

State the domain of f(x)=4x+3

  1. The bottom cannot be zero: x + 3 = 0 when x = -3.
  2. Every other number works.

The answer is (−∞,−3)∪(−3,∞).

Where students go wrong

Excluding the number printed in the formula instead of the one that breaks it. In 4/(x + 3) the bad input is -3, which makes the bottom zero, not 3.

Also called finding the domain, domain of a radical function or allowed input values.

What you can put on this worksheet

The domain of a square root
State the domain of f(x)=3x+7 → [−73,∞)
Rational, root-in-denominator and log
State the domain of f(x)=1x−1 → (−∞,1)∪(1,∞)

Questions about these worksheets

Yes. Every domain of a function 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 domain of a function 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 two 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: the domain of a square root and rational, root-in-denominator and log. Tick as many as you want and set how many of each, or let it spread them evenly.

Forgetting to flip the sign when the coefficient is negative. The domain of the square root of 12 - 3x is x at most 4, not x at least 4, because dividing by the negative turns the inequality round.