10.2 Graph Square Root Functions is a Grade 11 mathematics worksheet that builds skill with interpreting and graphing square root functions. Across 10 questions, students identify transformations such as reflections, shifts, stretches, and compressions; describe end behavior; determine domain and range; recognize function graphs; plot reference points; and draw graphs. The set includes five multiple-choice questions, one multiple-select question, two graphing tasks, one drawing task, and one open-ended domain-and-range response, giving students practice moving between symbolic descriptions, intervals, reference points, and visual representations.
This free printable worksheet with an answer key supports guided practice, independent work, review, or an assessment of students’ ability to connect algebraic features of square root functions to their graphs. Its combination of selected-response and constructed-response items helps teachers check both conceptual recognition and students’ ability to plot points and produce a graph. It is designed for Grade 11 mathematics instruction focused on graphing square root functions.
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10.2 Graph Square Root Functions
Total questions: 10
Name
Class
Date
1.
Describe the transformations for the function f(x)=−3x .
a)
The function is reflected over the x-axis and vertically stretched by a factor of 3.
b)
The function is vertically stretched by a factor of 2 and shifted down by 1 unit.
c)
The function is shifted to the right by 3 units and reflected over the x-axis.
d)
The function is reflected over the y-axis and vertically compressed by a factor of 3.
2.
Describe the end behavior for the function f(x)=52x+2 .
a)
As x approaches infinity, f(x) approaches infinity; as x approaches 0, f(x) approaches 2.
b)
As x approaches infinity, f(x) approaches 0; as x approaches 0, f(x) approaches 5.
c)
As x approaches infinity, f(x) approaches 10; as x approaches 0, f(x) approaches 1.
d)
As x approaches infinity, f(x) approaches 2; as x approaches 0, f(x) approaches infinity.
3.
Identify the domain and range of the function f(x)=2x+5−3 .
a)
Range: [2, infinity)
b)
Domain: [-5, infinity)
c)
Domain: [3, infinity)
d)
Range: [-3, infinity)
4.
Identify the graph for the function f(x)=21x+4−3 .
a)
b)
c)
d)
5.
Plot the reference points from the graph of the function: f(x)=−2x+1
6.
Graph the function: f(x)=2x+1
7.
Identify the domain and range for the function f(x)=−3x−1+4
a)
domain: (0, 1),
range: [4, ∞)
b)
domain: [1, 3],
range: [0, 4]
c)
domain: [1, ∞),
range: [4, ∞)
d)
domain: [1, ∞),
range: (-∞, 4]
8.
Describe the transformations in the function: f(x)=43x .
a)
The function is vertically stretched by a factor of 4.
b)
The function is reflected over the x-axis.
c)
The function is shifted 3 units to the right.
d)
The function is vertically compressed by a factor of 3/4.
9.
Identify the Domain and Range of f(x)=−3x .
4 lines
10.
Plot the points showing the location of the reference points from the function f(x)=2x+4+3
Answer Key
10.2 Graph Square Root Functions
Total questions: 10
1.
a) The function is reflected over the x-axis and vertically stretched by a factor of 3.
2.
a) As x approaches infinity, f(x) approaches infinity; as x approaches 0, f(x) approaches 2.
3.
b)
Domain: [-5, infinity)
, d)
Range: [-3, infinity)
4.
c)
5.
6.
n/a
7.
d)
domain: [1, ∞),
range: (-∞, 4]
8.
d) The function is vertically compressed by a factor of 3/4.
9.
n/a
10.
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FAQs
What does this square root functions worksheet cover?
This Grade 11 worksheet covers transformations, end behavior, domain and range, graph identification, reference points, and graphing for square root functions. Its 10 items combine multiple choice, multiple select, graphing, drawing, and open-ended questions so students apply both visual and algebraic ways of analyzing these functions.
How can I use this worksheet to teach graphing square root functions?
Begin by reviewing the parent square root graph and how a function’s equation changes its position, direction, and vertical scale. Use the transformation and domain-and-range items to model how students can predict graph features, then have them plot reference points and draw the graph in the worksheet’s graphing tasks. Finish by asking students to explain how the plotted points and endpoint support their domain, range, and end-behavior conclusions.
What mistakes should I watch for when students complete this square root functions worksheet?
Watch for students confusing horizontal shifts with vertical shifts, or interpreting a reflection as a stretch or compression. In the domain-and-range and end-behavior items, students may reverse the two sets of values or overlook the function’s endpoint and restricted input values. During the reference-point and drawing tasks, check that students plot the transformed points consistently before connecting them with the correct square root curve.
How do I assign and grade this square root functions worksheet?
The worksheet is available as a printable PDF and as a digital quiz on Wayground, and it includes a complete answer key for the multiple-choice, multiple-select, graphing, drawing, and open-ended items. Printable submissions can be graded by scanning student work with the Wayground for Teachers app. The PDF option also supports classrooms that want to reduce screen time while students practise graphing square root functions.
How can I differentiate this square root functions worksheet for my students?
Use the worksheet’s Advanced Settings to adjust font spacing or increase the font size, which can make the transformation prompts and graphing directions easier to follow. You can also enable a dyslexia-friendly font or translate the worksheet into another language when appropriate. These file-level changes can support access to the worksheet’s domain-and-range, reference-point, and graphing tasks without changing the questions.
Where can I find more worksheets like this on Wayground?
Wayground offers a broad collection of free printable worksheets and practice problems across subjects, with downloadable PDFs and answer keys to help students master essential skills and concepts. Teachers can browse more resources at https://wayground.com/en-us/worksheets.
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