A square root cannot take a negative, so the domain is whatever keeps the inside at zero or above. That turns every question into an inequality you already know how to solve.
The inside cannot be negative: 3x - 12 is at least 0.
Add 12, then divide by 3.
The answer is x≥4.
Where students go wrong
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.
Also called finding the domain, domain of a radical function or allowed input values.
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.
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.