Algebra 2 6-8 Guided Practice: Graphing Radical Functions

Last updated over 3 years ago

23 questions

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F.IF.7.b

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F.IF.7.b

Library

Algebra 2 6-8 Guided Practice: Graphing Radical Functions

Last updated over 3 years ago

23 questions

3

Solve It!

Solve It! Response & Explanation

3

Take Note: Take a moment to add the information about radical functions and square root functions to your notes. Don't forget to add the details from the Key Concept box about their reflections and transformations.

10

Problem 1 Got It? Graphing:
y=\sqrt{x} (parent square root function)
y=\sqrt{x}+2
y=\sqrt{x}-3
Graph the three square root functions on the same plane at desmos.com.
Zoom and pan your graph to establish an appropriate viewing window.
Notice how the translations relate to the parent function, to their graphs, and to one another.
Take a screenshot of your graph and upload or paste it onto the Formative canvas.

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8

Draggable item		Corresponding Item

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Problem 2 Got It? Graphing:
y=\sqrt{x} (parent square root function)
y=\sqrt{x-3}
y=\sqrt{x+2}
Graph the three square root functions on the same plane at desmos.com.
Zoom and pan your graph to establish an appropriate viewing window.
Notice how the translations relate to the parent function, to their graphs, and to one another.
Take a screenshot of your graph and upload or paste it onto the Formative canvas.

3

Take Note: Consider the parent square root function: 
and the combined transformation function: 
 

10

Problem 3 Got It? Graphing:
y=\sqrt{x} (parent square root function)
y=\frac{1}{2}\sqrt{x-3}+4
y=-2\sqrt{x+2}-1
Graph the three square root functions on the same plane at desmos.com.
Zoom and pan your graph to establish an appropriate viewing window.
Notice how the translations relate to the parent function, to their graphs, and to one another.
Take a screenshot of your graph and upload or paste it onto the Formative canvas.

3

10

3

10

Problem 5 Got It? Graphing:
y=\sqrt[3]{x} (parent cube root function)
y=3-\sqrt[3]{x-2}
Graph the two cube root functions on the same plane at desmos.com. FYI: You can access the \sqrt[n]{} button for custom indices in the Desmos math keyboard by clicking the Functions button.
Zoom and pan your graph to establish an appropriate viewing window.
Notice how the translations relate to the parent function, to their graphs, and to one another.
Take a screenshot of your graph and upload or paste it onto the Formative canvas.

3

10

Take Note: Summarize the process used in Problem 6 to rewrite the radical function y=\sqrt{9x+18} so that it can be graphed using transformations. You may use the canvas to help illustrate your written summary.

10

F.IF.7.b

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F.IF.7.b

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🧠 Retrieval Practice:
Summarize the mathematical content of this lesson. What topics, ideas, and vocabulary were introduced?

Video Check: Select all that apply with regards to the video embedded directly above this item.

🕵️ I carefully watched the entire video.

📵 I removed distractions from my field of view while watching the entire video.

🎧 I used headphones (or earbuds) to listen to the entire video as I watched it.

✋ I sought clarification, as needed, to understand each concept in the video.

🎓 I understand each concept in the video and feel ready to move on.

🎯 I feel prepared to complete challenging problems related to the video.

❌ None of these statements apply.

Solve It!

Solve It! Response & Explanation

Video Check: Select all that apply with regards to the video embedded directly above this item.

🕵️ I carefully watched the entire video.

📵 I removed distractions from my field of view while watching the entire video.

🎧 I used headphones (or earbuds) to listen to the entire video as I watched it.

✋ I sought clarification, as needed, to understand each concept in the video.

🎓 I understand each concept in the video and feel ready to move on.

🎯 I feel prepared to complete challenging problems related to the video.

❌ None of these statements apply.

Take Note: Take a moment to add the information about radical functions and square root functions to your notes. Don't forget to add the details from the Key Concept box about their reflections and transformations.

10

Take Note: What is the parent square root function ? Use y and x, as shown in this lesson.

10

Take Note: What is the parent radical function ? Use y, x, and index n, as shown in this lesson.

Problem 1 Got It? Graphing:
y=\sqrt{x} (parent square root function)
y=\sqrt{x}+2
y=\sqrt{x}-3
Graph the three square root functions on the same plane at desmos.com.
Zoom and pan your graph to establish an appropriate viewing window.
Notice how the translations relate to the parent function, to their graphs, and to one another.
Take a screenshot of your graph and upload or paste it onto the Formative canvas.

Video Check: Select all that apply with regards to the video embedded directly above this item.

🕵️ I carefully watched the entire video.

📵 I removed distractions from my field of view while watching the entire video.

🎧 I used headphones (or earbuds) to listen to the entire video as I watched it.

✋ I sought clarification, as needed, to understand each concept in the video.

🎓 I understand each concept in the video and feel ready to move on.

🎯 I feel prepared to complete challenging problems related to the video.

❌ None of these statements apply.

Take Note: Use your knowledge of function translations to match corresponding items below.

Draggable item		Corresponding Item
The graph of the parent function y=\sqrt{x} shifted up 3 units.		The graph of the parent function y=\sqrt{x} shifted right 3 units.
y=\sqrt{x-3}		The graph of the parent function y=\sqrt{x} shifted left 3 units.
y=\sqrt{x+3}		y=\sqrt{x}-3
The graph of the parent function y=\sqrt{x} shifted down 3 units.		y=\sqrt{x}+3

Problem 2 Got It? Graphing:
y=\sqrt{x} (parent square root function)
y=\sqrt{x-3}
y=\sqrt{x+2}
Graph the three square root functions on the same plane at desmos.com.
Zoom and pan your graph to establish an appropriate viewing window.
Notice how the translations relate to the parent function, to their graphs, and to one another.
Take a screenshot of your graph and upload or paste it onto the Formative canvas.

Video Check: Select all that apply with regards to the video embedded directly above this item.

🕵️ I carefully watched the entire video.

📵 I removed distractions from my field of view while watching the entire video.

🎧 I used headphones (or earbuds) to listen to the entire video as I watched it.

✋ I sought clarification, as needed, to understand each concept in the video.

🎓 I understand each concept in the video and feel ready to move on.

🎯 I feel prepared to complete challenging problems related to the video.

❌ None of these statements apply.

Take Note: Consider the parent square root function: 
and the combined transformation function: 
 

10

Take Note:
What impact does a in the combined transformation function have on the graph of the parent square root function ?

10

Take Note:
What impact does h in the combined transformation function have on the graph of the parent square root function ?

10

Take Note:
What impact does k in the combined transformation function have on the graph of the parent square root function ?

Take Note: Consider the parent square root function y=\sqrt{x} and the combined transformation function y=a\sqrt{x-h}+k. Match each parameter on the left with its effect on the graph of the parent function.

k
h
a

Translates the graph horizontally
Translates the graph vertically
Stretches or compresses the graph vertically and can cause a vertical reflection of the graph across the x-axis

Problem 3 Got It? Graphing:
y=\sqrt{x} (parent square root function)
y=\frac{1}{2}\sqrt{x-3}+4
y=-2\sqrt{x+2}-1
Graph the three square root functions on the same plane at desmos.com.
Zoom and pan your graph to establish an appropriate viewing window.
Notice how the translations relate to the parent function, to their graphs, and to one another.
Take a screenshot of your graph and upload or paste it onto the Formative canvas.

Video Check: Select all that apply with regards to the video embedded directly above this item.

🕵️ I carefully watched the entire video.

📵 I removed distractions from my field of view while watching the entire video.

🎧 I used headphones (or earbuds) to listen to the entire video as I watched it.

✋ I sought clarification, as needed, to understand each concept in the video.

🎓 I understand each concept in the video and feel ready to move on.

🎯 I feel prepared to complete challenging problems related to the video.

❌ None of these statements apply.

10

Video Check: Select all that apply with regards to the video embedded directly above this item.

🕵️ I carefully watched the entire video.

📵 I removed distractions from my field of view while watching the entire video.

🎧 I used headphones (or earbuds) to listen to the entire video as I watched it.

✋ I sought clarification, as needed, to understand each concept in the video.

🎓 I understand each concept in the video and feel ready to move on.

🎯 I feel prepared to complete challenging problems related to the video.

❌ None of these statements apply.

Problem 5 Got It? Graphing:
y=\sqrt[3]{x} (parent cube root function)
y=3-\sqrt[3]{x-2}
Graph the two cube root functions on the same plane at desmos.com. FYI: You can access the \sqrt[n]{} button for custom indices in the Desmos math keyboard by clicking the Functions button.
Zoom and pan your graph to establish an appropriate viewing window.
Notice how the translations relate to the parent function, to their graphs, and to one another.
Take a screenshot of your graph and upload or paste it onto the Formative canvas.

Video Check: Select all that apply with regards to the video embedded directly above this item.

🕵️ I carefully watched the entire video.

📵 I removed distractions from my field of view while watching the entire video.

🎧 I used headphones (or earbuds) to listen to the entire video as I watched it.

✋ I sought clarification, as needed, to understand each concept in the video.

🎓 I understand each concept in the video and feel ready to move on.

🎯 I feel prepared to complete challenging problems related to the video.

❌ None of these statements apply.

10

Take Note: Summarize the process used in Problem 6 to rewrite the radical function y=\sqrt{9x+18} so that it can be graphed using transformations. You may use the canvas to help illustrate your written summary.

Problem 6 Got It? How can you rewrite the cube root function below so that you can graph it using transformations. Describe the graph.

Stretch the graph of the parent function vertically by a factor of 2, translate 4 units left, and translate 2 units down.   

Stretch the graph of the parent function vertically by a factor of 2, translate 2 units left, and translate 4 units up.

Stretch the graph of the parent function vertically by a factor of 2, translate 4 units right, and translate 2 units down.

Problem 6 Got It? Reasoning: Describe the graph of y = |9x - 18| by rewriting it in the form y = a|x - h|. How is this similar to rewriting the square root equation below (from Problem 6)?

|9x - 18| = 9|x - 2|; the graph of y = 9|x - 2| is the graph of y = |x| stretched vertically by a factor of 9 and translated left 2 units; in both cases, you are rewriting the function so that x has a coefficient of 1.

|9x - 18| = 9|x - 2|; the graph of y = 9|x - 2| is the graph of y = |x| stretched vertically by a factor of 2 and translated right 9 units; in both cases, you are rewriting the function so that x has a coefficient of 1.

|9x - 18| = 9|x - 2|; the graph of y = 9|x - 2| is the graph of y = |x| stretched vertically by a factor of 9 and translated right 2 units; in both cases, you are rewriting the function so that x has a coefficient of 1.

10

🧠 Retrieval Practice:
Summarize the mathematical content of this lesson. What topics, ideas, and vocabulary were introduced?

Video Check: Select all that apply with regards to the video embedded directly above this item.

🕵️ I carefully watched the entire video.

📵 I removed distractions from my field of view while watching the entire video.

🎧 I used headphones (or earbuds) to listen to the entire video as I watched it.

✋ I sought clarification, as needed, to understand each concept in the video.

🎓 I understand each concept in the video and feel ready to move on.

🎯 I feel prepared to complete challenging problems related to the video.

❌ None of these statements apply.

Video Check: Select all that apply with regards to the video embedded directly above this item.

🕵️ I carefully watched the entire video.

📵 I removed distractions from my field of view while watching the entire video.

🎧 I used headphones (or earbuds) to listen to the entire video as I watched it.

✋ I sought clarification, as needed, to understand each concept in the video.

🎓 I understand each concept in the video and feel ready to move on.

🎯 I feel prepared to complete challenging problems related to the video.

❌ None of these statements apply.

Take Note: What is the parent square root function ? Use y and x, as shown in this lesson.

Take Note: What is the parent radical function ? Use y, x, and index n, as shown in this lesson.

Video Check: Select all that apply with regards to the video embedded directly above this item.

🕵️ I carefully watched the entire video.

📵 I removed distractions from my field of view while watching the entire video.

🎧 I used headphones (or earbuds) to listen to the entire video as I watched it.

✋ I sought clarification, as needed, to understand each concept in the video.

🎓 I understand each concept in the video and feel ready to move on.

🎯 I feel prepared to complete challenging problems related to the video.

❌ None of these statements apply.

Take Note: Use your knowledge of function translations to match corresponding items below.

The graph of the parent function y=\sqrt{x} shifted up 3 units.

The graph of the parent function y=\sqrt{x} shifted right 3 units.

y=\sqrt{x-3}

The graph of the parent function y=\sqrt{x} shifted left 3 units.

y=\sqrt{x+3}

y=\sqrt{x}-3

The graph of the parent function y=\sqrt{x} shifted down 3 units.

y=\sqrt{x}+3

Video Check: Select all that apply with regards to the video embedded directly above this item.

🕵️ I carefully watched the entire video.

📵 I removed distractions from my field of view while watching the entire video.

🎧 I used headphones (or earbuds) to listen to the entire video as I watched it.

✋ I sought clarification, as needed, to understand each concept in the video.

🎓 I understand each concept in the video and feel ready to move on.

🎯 I feel prepared to complete challenging problems related to the video.

❌ None of these statements apply.

Take Note:
What impact does a in the combined transformation function have on the graph of the parent square root function ?

Take Note:
What impact does h in the combined transformation function have on the graph of the parent square root function ?

Take Note:
What impact does k in the combined transformation function have on the graph of the parent square root function ?

Take Note: Consider the parent square root function y=\sqrt{x} and the combined transformation function y=a\sqrt{x-h}+k. Match each parameter on the left with its effect on the graph of the parent function.

k

h

a

Translates the graph horizontally

Translates the graph vertically

Stretches or compresses the graph vertically and can cause a vertical reflection of the graph across the x-axis

Video Check: Select all that apply with regards to the video embedded directly above this item.

🕵️ I carefully watched the entire video.

📵 I removed distractions from my field of view while watching the entire video.

🎧 I used headphones (or earbuds) to listen to the entire video as I watched it.

✋ I sought clarification, as needed, to understand each concept in the video.

🎓 I understand each concept in the video and feel ready to move on.

🎯 I feel prepared to complete challenging problems related to the video.

❌ None of these statements apply.

Problem 4 Got It? You can model the population P of Corpus Christi, Texas, between the years 1970 and 2005 by the radical function below.
Using this model, in what year was the population of Corpus Christi 275,000?

FYI: You can access the \sqrt[n]{} button for custom indices in the Desmos math keyboard by clicking the Functions button.

A

B

C

D

Video Check: Select all that apply with regards to the video embedded directly above this item.

🕵️ I carefully watched the entire video.

📵 I removed distractions from my field of view while watching the entire video.

🎧 I used headphones (or earbuds) to listen to the entire video as I watched it.

✋ I sought clarification, as needed, to understand each concept in the video.

🎓 I understand each concept in the video and feel ready to move on.

🎯 I feel prepared to complete challenging problems related to the video.

❌ None of these statements apply.

Video Check: Select all that apply with regards to the video embedded directly above this item.

🕵️ I carefully watched the entire video.

📵 I removed distractions from my field of view while watching the entire video.

🎧 I used headphones (or earbuds) to listen to the entire video as I watched it.

✋ I sought clarification, as needed, to understand each concept in the video.

🎓 I understand each concept in the video and feel ready to move on.

🎯 I feel prepared to complete challenging problems related to the video.

❌ None of these statements apply.

Problem 6 Got It? How can you rewrite the cube root function below so that you can graph it using transformations. Describe the graph. 

Stretch the graph of the parent function vertically by a factor of 2, translate 4 units left, and translate 2 units down.   

Stretch the graph of the parent function vertically by a factor of 2, translate 2 units left, and translate 4 units up.

Stretch the graph of the parent function vertically by a factor of 2, translate 4 units right, and translate 2 units down.

Problem 6 Got It? Reasoning: Describe the graph of y = |9x - 18| by rewriting it in the form y = a|x - h|. How is this similar to rewriting the square root equation below (from Problem 6)? 

|9x - 18| = 9|x - 2|; the graph of y = 9|x - 2| is the graph of y = |x| stretched vertically by a factor of 9 and translated left 2 units; in both cases, you are rewriting the function so that x has a coefficient of 1.

|9x - 18| = 9|x - 2|; the graph of y = 9|x - 2| is the graph of y = |x| stretched vertically by a factor of 2 and translated right 9 units; in both cases, you are rewriting the function so that x has a coefficient of 1.

|9x - 18| = 9|x - 2|; the graph of y = 9|x - 2| is the graph of y = |x| stretched vertically by a factor of 9 and translated right 2 units; in both cases, you are rewriting the function so that x has a coefficient of 1.

Problem 4 Got It? You can model the population P of Corpus Christi, Texas, between the years 1970 and 2005 by the radical function below.  
Using this model, in what year was the population of Corpus Christi 275,000?

 FYI: You can access the \sqrt[n]{} button for custom indices in the Desmos math keyboard by clicking the Functions button.

A

B

C

D

Algebra 2 6-8 Guided Practice: Graphing Radical Functions

Algebra 2 6-8 Guided Practice: Graphing Radical Functions

Solve It!

Solve It! Response & Explanation

Take Note: Summarize the process used in Problem 6 to rewrite the radical function y=\sqrt{9x+18} so that it can be graphed using transformations. You may use the canvas to help illustrate your written summary.

🧠 Retrieval Practice:Summarize the mathematical content of this lesson. What topics, ideas, and vocabulary were introduced?

Video Check: Select all that apply with regards to the video embedded directly above this item.

Solve It!

Solve It! Response & Explanation

Video Check: Select all that apply with regards to the video embedded directly above this item.

Take Note: What is the parent square root function ? Use y and x, as shown in this lesson.

Take Note: What is the parent radical function ? Use y, x, and index n, as shown in this lesson.

Video Check: Select all that apply with regards to the video embedded directly above this item.

Take Note: Use your knowledge of function translations to match corresponding items below.

Video Check: Select all that apply with regards to the video embedded directly above this item.

Take Note: What impact does a in the combined transformation function have on the graph of the parent square root function ?

Take Note: What impact does h in the combined transformation function have on the graph of the parent square root function ?

Take Note: What impact does k in the combined transformation function have on the graph of the parent square root function ?

Take Note: Consider the parent square root function y=\sqrt{x} and the combined transformation function y=a\sqrt{x-h}+k. Match each parameter on the left with its effect on the graph of the parent function.

Video Check: Select all that apply with regards to the video embedded directly above this item.

Video Check: Select all that apply with regards to the video embedded directly above this item.

Video Check: Select all that apply with regards to the video embedded directly above this item.

Take Note: Summarize the process used in Problem 6 to rewrite the radical function y=\sqrt{9x+18} so that it can be graphed using transformations. You may use the canvas to help illustrate your written summary.

Problem 6 Got It? How can you rewrite the cube root function below so that you can graph it using transformations. Describe the graph.

Problem 6 Got It? Reasoning: Describe the graph of y = |9x - 18| by rewriting it in the form y = a|x - h|. How is this similar to rewriting the square root equation below (from Problem 6)?

🧠 Retrieval Practice:Summarize the mathematical content of this lesson. What topics, ideas, and vocabulary were introduced?

Take Note: What is the parent square root function ? Use y and x, as shown in this lesson.

Take Note: What is the parent radical function ? Use y, x, and index n, as shown in this lesson.

Take Note: What impact does a in the combined transformation function have on the graph of the parent square root function ?

Take Note: What impact does h in the combined transformation function have on the graph of the parent square root function ?

Take Note: What impact does k in the combined transformation function have on the graph of the parent square root function ?

🧠 Retrieval Practice:
Summarize the mathematical content of this lesson. What topics, ideas, and vocabulary were introduced?

Take Note:
What impact does a in the combined transformation function have on the graph of the parent square root function ?

Take Note:
What impact does h in the combined transformation function have on the graph of the parent square root function ?

Take Note:
What impact does k in the combined transformation function have on the graph of the parent square root function ?

🧠 Retrieval Practice:
Summarize the mathematical content of this lesson. What topics, ideas, and vocabulary were introduced?

Take Note:
What impact does a in the combined transformation function have on the graph of the parent square root function ?

Take Note:
What impact does h in the combined transformation function have on the graph of the parent square root function ?

Take Note:
What impact does k in the combined transformation function have on the graph of the parent square root function ?