Graph y = sqrt(x - 5)

Starts at (5, 0), through (9, 2)

State the domain and range of y = 2sqrt(x - 6) - 3

Domain: x ≥ 6; range: y ≥ -3

State the domain and range of y = 2sqrt(x) - 5

Domain: x ≥ 0; range: y ≥ -5

State the domain and range of y = sqrt(x + 1) + 3

Domain: x ≥ -1; range: y ≥ 3

State the domain and range of y = sqrt(x - 4) - 3

Domain: x ≥ 4; range: y ≥ -3

Graph y = sqrt(x) + 1

Starts at (0, 1), through (4, 3)

State the domain and range of y = 3sqrt(x - 3) - 1

Domain: x ≥ 3; range: y ≥ -1

Graph y = sqrt(x - 1)

Starts at (1, 0), through (5, 2)

State the domain and range of y = sqrt(x + 2) - 1

Domain: x ≥ -2; range: y ≥ -1

State the domain and range of y = 2sqrt(x + 3) - 6

Domain: x ≥ -3; range: y ≥ -6

Graph y = sqrt(x - 4)

Starts at (4, 0), through (8, 2)

State the domain and range of y = 3sqrt(x + 1) - 3

Domain: x ≥ -1; range: y ≥ -3

Graph y = sqrt(x) + 4

Starts at (0, 4), through (4, 6)

State the domain and range of y = sqrt(x - 4) + 6

Domain: x ≥ 4; range: y ≥ 6

Center (0, -4), through (8, -2)

State the domain and range of y = 3sqrt(x) + 6

Domain: x ≥ 0; range: y ≥ 6

State the domain and range of y = 3sqrt(x) + 1

Domain: x ≥ 0; range: y ≥ 1

Worksheets · Algebra 1

Algebra 1 graphing radical and square root functions worksheet

A square root graph starts at the point where the inside is zero and curves off to the right; a cube root passes through that point and keeps going both ways. Find that point from h and k, then step to where the inside is 4 (or 8 for a cube root) to get a second point.

Select your difficulty

Pick more than one for a sheet that mixes them.



Sigma Prep · sigmaprep.io/worksheets Name Graphing Radical Functions Date Period Graph each function, or state its domain and range. Graph $y = \sqrt{x - 5}$ -10-10-5-55510100 State the domain and range of $y = 2 \sqrt{x - 6} - 3$ Graph $y = \sqrt{x - 3}$ -10-10-5-55510100 State the domain and range of $y = 2 \sqrt{x} - 5$ Graph $y = \sqrt[3]{x + 1}$ -10-10-5-55510100 State the domain and range of $y = \sqrt{x + 1} + 3$ Graph $y = \sqrt[3]{x + 3}$ -10-10-5-55510100 State the domain and range of $y = \sqrt{x - 4} - 3$ Graph $y = \sqrt{x} + 1$ -10-10-5-55510100 State the domain and range of $y = 3 \sqrt{x - 3} - 1$ Graph $y = \sqrt{x - 1}$ -10-10-5-55510100 State the domain and range of $y = \sqrt{x + 2} - 1$ Graph $y = \sqrt[3]{x} + 1$ -10-10-5-55510100 State the domain and range of $y = 2 \sqrt{x + 3} - 6$ Graph $y = \sqrt{x - 4}$ -10-10-5-55510100 State the domain and range of $y = 3 \sqrt{x + 1} - 3$ Graph $y = \sqrt{x} + 4$ -10-10-5-55510100 State the domain and range of $y = \sqrt{x - 4} + 6$ Graph $y = \sqrt[3]{x} - 4$ -10-10-5-55510100 State the domain and range of $y = 3 \sqrt{x} + 6$ 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.

Graph $y = \sqrt{x - 5}$ -10-10-5-55510100
State the domain and range of $y = 2 \sqrt{x - 6} - 3$
Graph $y = \sqrt{x - 3}$ -10-10-5-55510100
State the domain and range of $y = 2 \sqrt{x} - 5$
Graph $y = \sqrt[3]{x + 1}$ -10-10-5-55510100
State the domain and range of $y = \sqrt{x + 1} + 3$
Graph $y = \sqrt[3]{x + 3}$ -10-10-5-55510100
State the domain and range of $y = \sqrt{x - 4} - 3$
Graph $y = \sqrt{x} + 1$ -10-10-5-55510100
State the domain and range of $y = 3 \sqrt{x - 3} - 1$
Graph $y = \sqrt{x - 1}$ -10-10-5-55510100
State the domain and range of $y = \sqrt{x + 2} - 1$
Graph $y = \sqrt[3]{x} + 1$ -10-10-5-55510100
State the domain and range of $y = 2 \sqrt{x + 3} - 6$
Graph $y = \sqrt{x - 4}$ -10-10-5-55510100
State the domain and range of $y = 3 \sqrt{x + 1} - 3$
Graph $y = \sqrt{x} + 4$ -10-10-5-55510100
State the domain and range of $y = \sqrt{x - 4} + 6$
Graph $y = \sqrt[3]{x} - 4$ -10-10-5-55510100
State the domain and range of $y = 3 \sqrt{x} + 6$



Sigma Prep · sigmaprep.io/worksheets Name Graphing Radical FunctionsAnswer keyVersion 1 Date Period Graph each function, or state its domain and range. Graph $y = \sqrt{x - 5}$ -10-10-5-55510100Starts at $(5, 0)$ , through $(9, 2)$ State the domain and range of $y = 2 \sqrt{x - 6} - 3$ Domain: $x \geq 6$ ; range: $y \geq - 3$ Graph $y = \sqrt{x - 3}$ -10-10-5-55510100Starts at $(3, 0)$ , through $(7, 2)$ State the domain and range of $y = 2 \sqrt{x} - 5$ Domain: $x \geq 0$ ; range: $y \geq - 5$ Graph $y = \sqrt[3]{x + 1}$ -10-10-5-55510100Center $(- 1, 0)$ , through $(7, 2)$ State the domain and range of $y = \sqrt{x + 1} + 3$ Domain: $x \geq - 1$ ; range: $y \geq 3$ Graph $y = \sqrt[3]{x + 3}$ -10-10-5-55510100Center $(- 3, 0)$ , through $(5, 2)$ State the domain and range of $y = \sqrt{x - 4} - 3$ Domain: $x \geq 4$ ; range: $y \geq - 3$ Graph $y = \sqrt{x} + 1$ -10-10-5-55510100Starts at $(0, 1)$ , through $(4, 3)$ State the domain and range of $y = 3 \sqrt{x - 3} - 1$ Domain: $x \geq 3$ ; range: $y \geq - 1$ Graph $y = \sqrt{x - 1}$ -10-10-5-55510100Starts at $(1, 0)$ , through $(5, 2)$ State the domain and range of $y = \sqrt{x + 2} - 1$ Domain: $x \geq - 2$ ; range: $y \geq - 1$ Graph $y = \sqrt[3]{x} + 1$ -10-10-5-55510100Center $(0, 1)$ , through $(8, 3)$ State the domain and range of $y = 2 \sqrt{x + 3} - 6$ Domain: $x \geq - 3$ ; range: $y \geq - 6$ Graph $y = \sqrt{x - 4}$ -10-10-5-55510100Starts at $(4, 0)$ , through $(8, 2)$ State the domain and range of $y = 3 \sqrt{x + 1} - 3$ Domain: $x \geq - 1$ ; range: $y \geq - 3$ Graph $y = \sqrt{x} + 4$ -10-10-5-55510100Starts at $(0, 4)$ , through $(4, 6)$ State the domain and range of $y = \sqrt{x - 4} + 6$ Domain: $x \geq 4$ ; range: $y \geq 6$ Graph $y = \sqrt[3]{x} - 4$ -10-10-5-55510100Center $(0, - 4)$ , through $(8, - 2)$ State the domain and range of $y = 3 \sqrt{x} + 6$ Domain: $x \geq 0$ ; range: $y \geq 6$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Graphing Radical FunctionsAnswer keyVersion 1

Date Period

Graph each function, or state its domain and range.

Graph $y = \sqrt{x - 5}$ -10-10-5-55510100Starts at $(5, 0)$ , through $(9, 2)$
State the domain and range of $y = 2 \sqrt{x - 6} - 3$ Domain: $x \geq 6$ ; range: $y \geq - 3$
Graph $y = \sqrt{x - 3}$ -10-10-5-55510100Starts at $(3, 0)$ , through $(7, 2)$
State the domain and range of $y = 2 \sqrt{x} - 5$ Domain: $x \geq 0$ ; range: $y \geq - 5$
Graph $y = \sqrt[3]{x + 1}$ -10-10-5-55510100Center $(- 1, 0)$ , through $(7, 2)$
State the domain and range of $y = \sqrt{x + 1} + 3$ Domain: $x \geq - 1$ ; range: $y \geq 3$
Graph $y = \sqrt[3]{x + 3}$ -10-10-5-55510100Center $(- 3, 0)$ , through $(5, 2)$
State the domain and range of $y = \sqrt{x - 4} - 3$ Domain: $x \geq 4$ ; range: $y \geq - 3$
Graph $y = \sqrt{x} + 1$ -10-10-5-55510100Starts at $(0, 1)$ , through $(4, 3)$
State the domain and range of $y = 3 \sqrt{x - 3} - 1$ Domain: $x \geq 3$ ; range: $y \geq - 1$
Graph $y = \sqrt{x - 1}$ -10-10-5-55510100Starts at $(1, 0)$ , through $(5, 2)$
State the domain and range of $y = \sqrt{x + 2} - 1$ Domain: $x \geq - 2$ ; range: $y \geq - 1$
Graph $y = \sqrt[3]{x} + 1$ -10-10-5-55510100Center $(0, 1)$ , through $(8, 3)$
State the domain and range of $y = 2 \sqrt{x + 3} - 6$ Domain: $x \geq - 3$ ; range: $y \geq - 6$
Graph $y = \sqrt{x - 4}$ -10-10-5-55510100Starts at $(4, 0)$ , through $(8, 2)$
State the domain and range of $y = 3 \sqrt{x + 1} - 3$ Domain: $x \geq - 1$ ; range: $y \geq - 3$
Graph $y = \sqrt{x} + 4$ -10-10-5-55510100Starts at $(0, 4)$ , through $(4, 6)$
State the domain and range of $y = \sqrt{x - 4} + 6$ Domain: $x \geq 4$ ; range: $y \geq 6$
Graph $y = \sqrt[3]{x} - 4$ -10-10-5-55510100Center $(0, - 4)$ , through $(8, - 2)$
State the domain and range of $y = 3 \sqrt{x} + 6$ Domain: $x \geq 0$ ; range: $y \geq 6$

How to do these

Graph $y = \sqrt{x - 3} + 1$

The inside is zero at x = 3, so the graph starts at (3, 1).
At x = 7 the inside is 4, whose root is 2, giving (7, 3).
Curve through them, flattening out.

The answer is Starts at $(3, 1)$ , through $(7, 3)$ .

Where students go wrong

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

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 $y = \sqrt{x} + 1$ → Starts at $(0, 1)$ , through $(4, 3)$
Domain and range: State the domain and range of $y = 3 \sqrt{x} + 1$ → Domain: $x \geq 0$ ; range: $y \geq 1$

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 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: a square root or cube root function and domain and range. 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.

Algebra 1 graphing radical and square root functions worksheet

Select your difficulty

Graphing Radical Functions

Graphing Radical FunctionsAnswer keyVersion 1

How to do these

Where students go wrong

What you can put on this worksheet

Questions about these worksheets

Are these graphing radical and square root functions worksheets free?+

Do the graphing radical and square root functions worksheets come with an answer key?+

Are these graphing radical and square root functions worksheets printable?+

What grade are these graphing radical and square root functions worksheets for?+

Can I get a different version of the same graphing radical and square root functions worksheet?+

Is this a free alternative to Kuta Software for graphing radical and square root functions?+

Can I choose how hard the graphing radical and square root functions questions are?+

What kinds of question are on a graphing radical and square root functions worksheet?+

What do students get wrong with graphing radical and square root functions?+