Worksheets · Algebra 1

Graphing radical and square root functions worksheet for Algebra 1

Algebra 1 meets the square root and cube root functions as parent graphs and their shifts. Most of the graphs here are cube roots, which have no endpoint and bend through a center point; square roots start at an endpoint. Make a short table using x-values that put perfect squares or cubes inside the root, plot a few points, and state the domain and range of the square root functions as inequalities.

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.

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

Sigma Prep · sigmaprep.io/worksheets

Name

Graphing Radical Functions

Date Period

Graph each function, or state its domain and range.

  1. Graph a square or cube root function

    Graph y=x+3−10−10−5−5551010
  2. Graph y=x−4−10−10−5−5551010
  3. Graph y=x+53−10−10−5−5551010
  4. Graph y=x3+4−10−10−5−5551010
  5. Graph y=x−13−10−10−5−5551010
  6. Graph y=x3−2−10−10−5−5551010
  7. Graph y=x3−3−10−10−5−5551010
  8. Graph y=x+43−10−10−5−5551010
  9. Graph y=x−23−10−10−5−5551010
  10. Graph y=x+33−10−10−5−5551010

  1. Find the domain and range

    State the domain and range of y=2x−5+2
  2. State the domain and range of y=3x+4−1
  3. State the domain and range of y=3x+1+2
  4. State the domain and range of y=x+1+6
  5. State the domain and range of y=x−6−3
  6. State the domain and range of y=3x−3−6
  7. State the domain and range of y=x+2−3
  8. State the domain and range of y=3x+4
  9. State the domain and range of y=x−1+4
  10. State the domain and range of y=x−2

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

Sigma Prep · sigmaprep.io/worksheets

Name

Graphing Radical FunctionsAnswer keyVersion 2

Date Period

Graph each function, or state its domain and range.

  1. Graph a square or cube root function

    Graph y=x+3−10−10−5−5551010Starts at (−3,0), through (1,2)
  2. Graph y=x−4−10−10−5−5551010Starts at (0,−4), through (4,−2)
  3. Graph y=x+53−10−10−5551010Center (−5,0), through (3,2)
  4. Graph y=x3+4−10−10−5−5551010Center (0,4), through (8,6)
  5. Graph y=x−13−10−10−5−5551010Center (1,0), through (9,2)
  6. Graph y=x3−2−10−10−5−5551010Center (0,−2), through (8,0)
  7. Graph y=x3−3−10−10−5−5510510Center (0,−3), through (8,−1)
  8. Graph y=x+43−10−10−5551010−5Center (−4,0), through (4,2)
  9. Graph y=x−23−10−10−5−5551010Center (2,0), through (10,2)
  10. Graph y=x+33−10−10−5551010−5Center (−3,0), through (5,2)

  1. Find the domain and range

    State the domain and range of y=2x−5+2Domain: x≥5; range: y≥2
  2. State the domain and range of y=3x+4−1Domain: x≥−4; range: y≥−1
  3. State the domain and range of y=3x+1+2Domain: x≥−1; range: y≥2
  4. State the domain and range of y=x+1+6Domain: x≥−1; range: y≥6
  5. State the domain and range of y=x−6−3Domain: x≥6; range: y≥−3
  6. State the domain and range of y=3x−3−6Domain: x≥3; range: y≥−6
  7. State the domain and range of y=x+2−3Domain: x≥−2; range: y≥−3
  8. State the domain and range of y=3x+4Domain: x≥0; range: y≥4
  9. State the domain and range of y=x−1+4Domain: x≥1; range: y≥4
  10. State the domain and range of y=x−2Domain: x≥0; range: y≥−2

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

How to do these

State the domain and range of y=x+2−1

  1. The inside must be at least 0: x + 2 ≥ 0, so x ≥ -2.
  2. The root is never negative, so y is at least -1.

The answer is Domain: x≥−2; range: y≥−1.

Where students go wrong

Shifting the graph the wrong way. In y = √(x + 2) the inside is zero at x = -2, so the graph starts 2 units to the left, not the right.

Also called graphing square root functions, cube root graphs or radical function transformations.

What you can put on this worksheet

A square root or cube root function
Graph y=x+1 → Starts at (0,1), through (4,3)
Domain and range
State the domain and range of y=3x+1 → Domain: x≥0; range: y≥1
A fraction in front
Graph, and give the domain and range:
y=23x−1 → Domain: x≥1Range: y≥0

Questions about these worksheets

Yes. Every graphing radical and square root functions 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 graphing radical and square root functions 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 3: a square root or cube root function, domain and range and a fraction in front. Tick as many as you want and set how many of each, or let it spread them evenly.

Starting a square root at the origin no matter what is inside. The start moves with h, and to the right for x - 3.