State the domain of f(x) = (-5)/(x - 3)

(-infinity, 3) or (3, infinity)

State the domain of f(x) = (5)/(x + 5)

(-infinity, -5) or (-5, infinity)

State the domain of f(x) = 6/x

(-infinity, 0) or (0, infinity)

State the domain of f(x) = (8)/(x - 2)

(-infinity, 2) or (2, infinity)

State the domain of f(x) = (-1)/(x + 1)

(-infinity, -1) or (-1, infinity)

State the domain of f(x) = (9)/(x - 6)

(-infinity, 6) or (6, infinity)

State the domain of f(x) = (-8)/(x + 4)

(-infinity, -4) or (-4, infinity)

State the domain of f(x) = (-4)/(x - 1)

(-infinity, 1) or (1, infinity)

State the domain of f(x) = (-8)/(x + 3)

(-infinity, -3) or (-3, infinity)

State the domain of f(x) = (1)/(x + 2)

(-infinity, -2) or (-2, infinity)

State the domain of f(x) = (1)/(x - 1)

(-infinity, 1) or (1, infinity)

Worksheets · Precalculus

Domain of a function worksheet for Precalculus

Precalculus collects the restrictions a formula carries: a square root needs a non-negative inside, and a denominator, often a quadratic to factor, cannot be zero. Every answer is written in interval notation.

Also taught in Algebra 2 and Algebra 1, 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.



Sigma Prep · sigmaprep.io/worksheets Name Domain of a Function Date Period State the domain in interval notation. Find the domain of a square root function State the domain of $f (x) = \sqrt{3 x - 5}$ State the domain of $f (x) = \sqrt{x - 5}$ State the domain of $f (x) = \sqrt{4 x + 3}$ State the domain of $f (x) = \sqrt{2 x + 2}$ State the domain of $f (x) = \sqrt{2 x - 3}$ State the domain of $f (x) = \sqrt{4 x - 9}$ State the domain of $f (x) = \sqrt{2 x + 5}$ State the domain of $f (x) = \sqrt{2 x + 4}$ State the domain of $f (x) = \sqrt{4 x - 5}$ State the domain of $f (x) = \sqrt{x + 8}$ Find the domain when the variable is in a denominator State the domain of $f (x) = \frac{- 5}{x - 3}$ State the domain of $f (x) = \frac{5}{x + 5}$ State the domain of $f (x) = \frac{6}{x}$ State the domain of $f (x) = \frac{8}{x - 2}$ State the domain of $f (x) = \frac{- 1}{x + 1}$ State the domain of $f (x) = \frac{9}{x - 6}$ State the domain of $f (x) = \frac{- 8}{x + 4}$ State the domain of $f (x) = \frac{- 4}{x - 1}$ State the domain of $f (x) = \frac{- 8}{x + 3}$ State the domain of $f (x) = \frac{1}{x + 2}$ 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.

Find the domain of a square root function
State the domain of $f (x) = \sqrt{3 x - 5}$
State the domain of $f (x) = \sqrt{x - 5}$
State the domain of $f (x) = \sqrt{4 x + 3}$
State the domain of $f (x) = \sqrt{2 x + 2}$
State the domain of $f (x) = \sqrt{2 x - 3}$
State the domain of $f (x) = \sqrt{4 x - 9}$
State the domain of $f (x) = \sqrt{2 x + 5}$
State the domain of $f (x) = \sqrt{2 x + 4}$
State the domain of $f (x) = \sqrt{4 x - 5}$
State the domain of $f (x) = \sqrt{x + 8}$

Find the domain when the variable is in a denominator
State the domain of $f (x) = \frac{- 5}{x - 3}$
State the domain of $f (x) = \frac{5}{x + 5}$
State the domain of $f (x) = \frac{6}{x}$
State the domain of $f (x) = \frac{8}{x - 2}$
State the domain of $f (x) = \frac{- 1}{x + 1}$
State the domain of $f (x) = \frac{9}{x - 6}$
State the domain of $f (x) = \frac{- 8}{x + 4}$
State the domain of $f (x) = \frac{- 4}{x - 1}$
State the domain of $f (x) = \frac{- 8}{x + 3}$
State the domain of $f (x) = \frac{1}{x + 2}$



Sigma Prep · sigmaprep.io/worksheets Name Domain of a FunctionAnswer keyVersion 3 Date Period State the domain in interval notation. Find the domain of a square root function State the domain of $f (x) = \sqrt{3 x - 5}$ $[\frac{5}{3}, \infty)$ State the domain of $f (x) = \sqrt{x - 5}$ $[5, \infty)$ State the domain of $f (x) = \sqrt{4 x + 3}$ $[- \frac{3}{4}, \infty)$ State the domain of $f (x) = \sqrt{2 x + 2}$ $[- 1, \infty)$ State the domain of $f (x) = \sqrt{2 x - 3}$ $[\frac{3}{2}, \infty)$ State the domain of $f (x) = \sqrt{4 x - 9}$ $[\frac{9}{4}, \infty)$ State the domain of $f (x) = \sqrt{2 x + 5}$ $[- \frac{5}{2}, \infty)$ State the domain of $f (x) = \sqrt{2 x + 4}$ $[- 2, \infty)$ State the domain of $f (x) = \sqrt{4 x - 5}$ $[\frac{5}{4}, \infty)$ State the domain of $f (x) = \sqrt{x + 8}$ $[- 8, \infty)$ Find the domain when the variable is in a denominator State the domain of $f (x) = \frac{- 5}{x - 3}$ $(- \infty, 3) \cup (3, \infty)$ State the domain of $f (x) = \frac{5}{x + 5}$ $(- \infty, - 5) \cup (- 5, \infty)$ State the domain of $f (x) = \frac{6}{x}$ $(- \infty, 0) \cup (0, \infty)$ State the domain of $f (x) = \frac{8}{x - 2}$ $(- \infty, 2) \cup (2, \infty)$ State the domain of $f (x) = \frac{- 1}{x + 1}$ $(- \infty, - 1) \cup (- 1, \infty)$ State the domain of $f (x) = \frac{9}{x - 6}$ $(- \infty, 6) \cup (6, \infty)$ State the domain of $f (x) = \frac{- 8}{x + 4}$ $(- \infty, - 4) \cup (- 4, \infty)$ State the domain of $f (x) = \frac{- 4}{x - 1}$ $(- \infty, 1) \cup (1, \infty)$ State the domain of $f (x) = \frac{- 8}{x + 3}$ $(- \infty, - 3) \cup (- 3, \infty)$ State the domain of $f (x) = \frac{1}{x + 2}$ $(- \infty, - 2) \cup (- 2, \infty)$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Domain of a FunctionAnswer keyVersion 3

Date Period

State the domain in interval notation.

Find the domain of a square root function
State the domain of $f (x) = \sqrt{3 x - 5}$ $[\frac{5}{3}, \infty)$
State the domain of $f (x) = \sqrt{x - 5}$ $[5, \infty)$
State the domain of $f (x) = \sqrt{4 x + 3}$ $[- \frac{3}{4}, \infty)$
State the domain of $f (x) = \sqrt{2 x + 2}$ $[- 1, \infty)$
State the domain of $f (x) = \sqrt{2 x - 3}$ $[\frac{3}{2}, \infty)$
State the domain of $f (x) = \sqrt{4 x - 9}$ $[\frac{9}{4}, \infty)$
State the domain of $f (x) = \sqrt{2 x + 5}$ $[- \frac{5}{2}, \infty)$
State the domain of $f (x) = \sqrt{2 x + 4}$ $[- 2, \infty)$
State the domain of $f (x) = \sqrt{4 x - 5}$ $[\frac{5}{4}, \infty)$
State the domain of $f (x) = \sqrt{x + 8}$ $[- 8, \infty)$

Find the domain when the variable is in a denominator
State the domain of $f (x) = \frac{- 5}{x - 3}$ $(- \infty, 3) \cup (3, \infty)$
State the domain of $f (x) = \frac{5}{x + 5}$ $(- \infty, - 5) \cup (- 5, \infty)$
State the domain of $f (x) = \frac{6}{x}$ $(- \infty, 0) \cup (0, \infty)$
State the domain of $f (x) = \frac{8}{x - 2}$ $(- \infty, 2) \cup (2, \infty)$
State the domain of $f (x) = \frac{- 1}{x + 1}$ $(- \infty, - 1) \cup (- 1, \infty)$
State the domain of $f (x) = \frac{9}{x - 6}$ $(- \infty, 6) \cup (6, \infty)$
State the domain of $f (x) = \frac{- 8}{x + 4}$ $(- \infty, - 4) \cup (- 4, \infty)$
State the domain of $f (x) = \frac{- 4}{x - 1}$ $(- \infty, 1) \cup (1, \infty)$
State the domain of $f (x) = \frac{- 8}{x + 3}$ $(- \infty, - 3) \cup (- 3, \infty)$
State the domain of $f (x) = \frac{1}{x + 2}$ $(- \infty, - 2) \cup (- 2, \infty)$

How to do these

State the domain of $f (x) = \frac{x + 3}{x^{2} - 7 x + 10}$

Factor the bottom: x² - 7x + 10 = (x - 2)(x - 5).
It is zero at x = 2 and at x = 5, so both are left out.
Every other number works, which takes three intervals.

The answer is $(- \infty, 2) \cup (2, 5) \cup (5, \infty)$ .

Where students go wrong

Stopping at one excluded value. x² - 7x + 10 factors as (x - 2)(x - 5), so the bottom is zero at both 2 and 5, and the domain needs three intervals, not two.

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 $f (x) = \sqrt{3 x + 7}$ → $[- \frac{7}{3}, \infty)$
Rational, root-in-denominator and log: State the domain of $f (x) = \frac{1}{x - 1}$ → $(- \infty, 1) \cup (1, \infty)$

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.

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 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.

Domain of a function worksheet for Precalculus

Select your difficulty

Find the domain of a square root function

Find the domain when the variable is in a denominator

Find the domain of a square root function

Find the domain when the variable is in a denominator

How to do these

Where students go wrong

What you can put on this worksheet

Questions about these worksheets

Are these domain of a function worksheets free?+

Do the domain of a function worksheets come with an answer key?+

Are these domain of a function worksheets printable?+

What grade are these domain of a function worksheets for?+

Can I get a different version of the same domain of a function worksheet?+

Is this a free alternative to Kuta Software for domain of a function?+

Can I choose how hard the domain of a function questions are?+

What kinds of question are on a domain of a function worksheet?+

What do students get wrong with domain of a function?+