Algebra 2 8-2 Guided Practice: The Reciprocal Function Family

Last updated over 3 years ago

25 questions

3

10

F.BF.3

3

9

20

F.BF.3

10

3

20

F.BF.3

3

10

F.BF.3

3

15

A.CED.2

F.BF.3

15

A.CED.2

F.BF.3

Library

Algebra 2 8-2 Guided Practice: The Reciprocal Function Family

Last updated over 3 years ago

25 questions

3

10

F.BF.3

3

10

Take Note: Define reciprocal function.

5

9

Draggable item		Corresponding Item

20

F.BF.3

10

Problem 1 Got It?

Graph the three functions on the same plane at desmos.com.
Zoom and pan your graph to establish an appropriate viewing window. Consider the similarities and differences between the graphs.
Think about the domain, range, intercepts, asymptotes, etc., and how they relate to the equation of each function.
Take a screenshot of your graph and upload or paste it onto the Formative canvas.
y=\frac{6}{x}, y=\frac{8}{x}, y=\frac{12}{x}

3

10

Take Note: What is a branch of a graph of a reciprocal function?

10

F.BF.3

10

F.BF.3

10

F.BF.3

3

5

Take Note: How does the parameter h relate to the asymptotes of a translated reciprocal function?

5

20

Problem 3 Got It? What is the graph of the function? Identify its domain and range on the canvas. Include graph detail.
Use Desmos to check your work and make any necessary edits AFTER first graphing by hand.

F.BF.3

3

10

Take Note: Summarize the process of writing the equation of a transformed reciprocal function from its asymptotes (as demonstrated in Problem 4).

10

F.BF.3

3

15

A.CED.2

F.BF.3

15

A.CED.2

F.BF.3

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.

Solve It! For a class party, the students will share the cost for the hall rental. Each student will also have to pay $8 for food. The cost of the hall rental is already graphed. What effect does the food cost have on the graph?

The additional $8 charge for food per student causes a translation of the graph left 8 units.

The additional $8 charge for food per student causes a translation of the graph right 8 units.

The additional $8 charge for food per student causes a translation of the graph down 8 units.

The additional $8 charge for food per student causes a translation of the graph up 8 units.

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: Define reciprocal function.

5

Take Note: Provide an example of a reciprocal function.

Take Note: Consider the general form of the reciprocal function family y=\frac{a}{x-h}+k.

Match each parameter with the transformational impact it has on the parent function.

Draggable item		Corresponding Item
h		Vertical scaling & reflection
k		Horizontal translation
a		Vertical translation

Problem 1 Got It? Which statements below are true regarding the graph of the function?
Select all that apply.

The graph of the function is: 

The range of the graph is all real numbers.

The graph has no y-intercept.

The x-intercept of the graph is (-12, 0).

The horizontal asymptote of the graph is y = 0.

The graph of the function is:

The domain of the graph is all real numbers except x = 0.

The domain of the graph is all real numbers.

The vertical asymptote of the graph is x = 12.

Problem 1 Got It?

Graph the three functions on the same plane at desmos.com.
Zoom and pan your graph to establish an appropriate viewing window. Consider the similarities and differences between the graphs.
Think about the domain, range, intercepts, asymptotes, etc., and how they relate to the equation of each function.
Take a screenshot of your graph and upload or paste it onto the Formative canvas.
y=\frac{6}{x}, y=\frac{8}{x}, y=\frac{12}{x}

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: What is a branch of a graph of a reciprocal function?

10

Take Note: Sketch a reciprocal function with asymptotes at x=-3 and y=5.

10

F.BF.3

10

F.BF.3

10

F.BF.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.

5

Take Note: How does the parameter h relate to the asymptotes of a translated reciprocal function?

5

Take Note: How does the parameter k relate to the asymptotes of a translated reciprocal function?

Problem 3 Got It? What is the graph of the function? Identify its domain and range on the canvas. Include graph detail.
Use Desmos to check your work and make any necessary edits AFTER first graphing by hand.

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 of writing the equation of a transformed reciprocal function from its asymptotes (as demonstrated in Problem 4).

Problem 4 Got It? The graph below is a translation of the graph of

What is an equation of the function?

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? The junior class is renting a laser tag facility with a capacity of 325 people. The cost for the facility is $1200. The party must have 13 adult chaperones.

Respond to each question on the right with the appropriate response from the left.

All real numbers
Whole numbers from 1 to 312
Integers from -13 to 325
173 students
162 students
160 students

If every student who attends shares the facility cost equally, what function models the cost per student C with respect to the number of students n who attend?
What is the domain of the function? Consider only the domain values that make sense in the context of the problem.
How many students must attend to make the cost per student no more than $7.50 per student?

Problem 5 Got It? The junior class is renting a laser tag facility with a capacity of 325 people. The cost for the facility is $1200. The party must have 13 adult chaperones.

Respond to each question on the right with the appropriate response from the left.

All real numbers
Whole numbers from 1 to 282
190 students
172 students
165 students

Suppose the class wants to promote the event by giving away 30 free admissions to the event. What new function models the cost per student C with respect to the number of students n who attend?
What is the domain of the new function, with 30 tickets to be given away? Consider only the domain values that make sense in the context of the problem.
now, how many students must attend to make the cost per student no more than $7.50 per student?

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.

Solve It! For a class party, the students will share the cost for the hall rental. Each student will also have to pay $8 for food. The cost of the hall rental is already graphed. What effect does the food cost have on the graph? 

The additional $8 charge for food per student causes a translation of the graph left 8 units.

The additional $8 charge for food per student causes a translation of the graph right 8 units.

The additional $8 charge for food per student causes a translation of the graph down 8 units.

The additional $8 charge for food per student causes a translation of the graph up 8 units.

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: Provide an example of a reciprocal function.

Take Note: Consider the general form of the reciprocal function family y=\frac{a}{x-h}+k.

Match each parameter with the transformational impact it has on the parent function.

h

Vertical scaling & reflection

k

Horizontal translation

a

Vertical translation

Problem 1 Got It? Which statements below are true regarding the graph of the function? 
Select all that apply.

The graph of the function is: 

The range of the graph is all real numbers.

The graph has no y-intercept.

The x-intercept of the graph is (-12, 0).

The horizontal asymptote of the graph is y = 0.

The graph of the function is:

The domain of the graph is all real numbers except x = 0.

The domain of the graph is all real numbers.

The vertical asymptote of the graph is x = 12.

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: Sketch a reciprocal function with asymptotes at x=-3 and y=5.

Problem 2 Got It?

A

B

C

D

Problem 2 Got It?

A

B

C

D

Problem 2 Got It?

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.

Take Note: How does the parameter k relate to the asymptotes of a translated reciprocal function?

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? The graph below is a translation of the graph of 

What is an equation of the function?

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? The junior class is renting a laser tag facility with a capacity of 325 people. The cost for the facility is $1200. The party must have 13 adult chaperones.

Respond to each question on the right with the appropriate response from the left.

All real numbers

Whole numbers from 1 to 312

Integers from -13 to 325

173 students

162 students

160 students

If every student who attends shares the facility cost equally, what function models the cost per student C with respect to the number of students n who attend?

What is the domain of the function? Consider only the domain values that make sense in the context of the problem.

How many students must attend to make the cost per student no more than $7.50 per student?

Problem 5 Got It? The junior class is renting a laser tag facility with a capacity of 325 people. The cost for the facility is $1200. The party must have 13 adult chaperones.

Respond to each question on the right with the appropriate response from the left.

All real numbers

Whole numbers from 1 to 282

190 students

172 students

165 students

Suppose the class wants to promote the event by giving away 30 free admissions to the event. What new function models the cost per student C with respect to the number of students n who attend?

What is the domain of the new function, with 30 tickets to be given away? Consider only the domain values that make sense in the context of the problem.

now, how many students must attend to make the cost per student no more than $7.50 per student?

Problem 2 Got It?

A

B

C

D

Problem 2 Got It?

A

B

C

D

Problem 2 Got It?

A

B

C

D

Algebra 2 8-2 Guided Practice: The Reciprocal Function Family

Algebra 2 8-2 Guided Practice: The Reciprocal Function Family

Take Note: Define reciprocal function.

Take Note: What is a branch of a graph of a reciprocal function?

Take Note: How does the parameter h relate to the asymptotes of a translated reciprocal function?

Problem 3 Got It? What is the graph of the function? Identify its domain and range on the canvas. Include graph detail. Use Desmos to check your work and make any necessary edits AFTER first graphing by hand.

Take Note: Summarize the process of writing the equation of a transformed reciprocal function from its asymptotes (as demonstrated in Problem 4).

🧠 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! For a class party, the students will share the cost for the hall rental. Each student will also have to pay $8 for food. The cost of the hall rental is already graphed. What effect does the food cost have on the graph?

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

Take Note: Define reciprocal function.

Take Note: Provide an example of a reciprocal function.

Take Note: Consider the general form of the reciprocal function family y=\frac{a}{x-h}+k.Match each parameter with the transformational impact it has on the parent function.

Problem 1 Got It? Which statements below are true regarding the graph of the function? Select all that apply.

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

Take Note: What is a branch of a graph of a reciprocal function?

Take Note: Sketch a reciprocal function with asymptotes at x=-3 and y=5.

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

Take Note: How does the parameter h relate to the asymptotes of a translated reciprocal function?

Take Note: How does the parameter k relate to the asymptotes of a translated reciprocal function?

Problem 3 Got It? What is the graph of the function? Identify its domain and range on the canvas. Include graph detail. Use Desmos to check your work and make any necessary edits AFTER first graphing by hand.

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

Take Note: Summarize the process of writing the equation of a transformed reciprocal function from its asymptotes (as demonstrated in Problem 4).

Problem 4 Got It? The graph below is a translation of the graph of What is an equation of the function?

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

Problem 5 Got It? The junior class is renting a laser tag facility with a capacity of 325 people. The cost for the facility is $1200. The party must have 13 adult chaperones.Respond to each question on the right with the appropriate response from the left.

Problem 5 Got It? The junior class is renting a laser tag facility with a capacity of 325 people. The cost for the facility is $1200. The party must have 13 adult chaperones.Respond to each question on the right with the appropriate response from the left.

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

Take Note: Provide an example of a reciprocal function.

Take Note: Sketch a reciprocal function with asymptotes at x=-3 and y=5.

Problem 2 Got It?

Problem 2 Got It?

Problem 2 Got It?

Take Note: How does the parameter k relate to the asymptotes of a translated reciprocal function?

Problem 3 Got It? What is the graph of the function? Identify its domain and range on the canvas. Include graph detail.
Use Desmos to check your work and make any necessary edits AFTER first graphing by hand.

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

Take Note: Consider the general form of the reciprocal function family y=\frac{a}{x-h}+k.

Match each parameter with the transformational impact it has on the parent function.

Problem 1 Got It? Which statements below are true regarding the graph of the function?
Select all that apply.

Problem 3 Got It? What is the graph of the function? Identify its domain and range on the canvas. Include graph detail.
Use Desmos to check your work and make any necessary edits AFTER first graphing by hand.

Problem 4 Got It? The graph below is a translation of the graph of

What is an equation of the function?

Problem 5 Got It? The junior class is renting a laser tag facility with a capacity of 325 people. The cost for the facility is $1200. The party must have 13 adult chaperones.

Respond to each question on the right with the appropriate response from the left.

Problem 5 Got It? The junior class is renting a laser tag facility with a capacity of 325 people. The cost for the facility is $1200. The party must have 13 adult chaperones.

Respond to each question on the right with the appropriate response from the left.

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