Algebra 2 6-6 Guided Practice: Function Operations

Last updated over 3 years ago

17 questions

3

5

F.BF.1.b

3

8

3

9

3

5

F.BF.1.b

F.BF.1.c

5

F.BF.1.b

F.BF.1.c

5

F.BF.1.b

F.BF.1.c

Library

Algebra 2 6-6 Guided Practice: Function Operations

Last updated over 3 years ago

17 questions

3

5

F.BF.1.b

Take Note: Take a moment to record the function operations in your notes.

3

8

Draggable item		Corresponding Item

10

F.BF.1.b

3

10

F.BF.1.b

3

10

Take Note: What is a composite function ?

You may use the canvas to help illustrate your written response.

9

Draggable item		Corresponding Item

10

F.BF.1.b

F.BF.1.c

3

5

F.BF.1.b

F.BF.1.c

5

F.BF.1.b

F.BF.1.c

5

F.BF.1.b

F.BF.1.c

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! You want to buy a sofa that was marked down by $50 before the clearance discount was applied.

The furniture store may add the 5% sales tax before applying the additional discount, or it may add the sales tax after applying the additional discount. Which way is better for you, the customer?

After

Before

Take Note: Take a moment to record the function operations in your notes.

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 the properties of function operations to match equivalent expressions.

Draggable item		Corresponding Item
h(x)-g(x)		\frac{h(x)}{g(x)}
f(x)+g(x)		(h-g)(x)
(\frac{h}{g})(x)		h(x)\cdot g(x)
(h\cdot g)(x)		(f+g)(x)

10

F.BF.1.b

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

F.BF.1.b

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 composite function ?

You may use the canvas to help illustrate your written response.

Take Note: Consider functions f(x) and g(x) and the composite function g(f(x)).
Match equivalent items below.

Draggable item		Corresponding Item
g(f(x))		x
Domain of f(x)		Range of f(x)
Domain of g(f(x))		(g\circ f)(x)

10

F.BF.1.b

F.BF.1.c

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

Problem 4 Got It? A store is offering a 15% discount on all items. Also, employees get a 20% discount (20% off original price(s)). Write a composite function to model taking the 15% discount and then the 20% discount.

Let D(x) = cost after applying the 15% discount, E(x) = cost after applying the 20% employee discount, and x = cost of item(s). Then D(x) = 0.80x and E(x) = 0.85x. (E ◦ D)(x) = 0.68x.

Let D(x) = cost after applying the 15% discount, E(x) = cost after applying the 20% employee discount, and x = cost of item(s). Then D(x) = 0.85x and E(x) = 0.80x. (E ◦ D)(x) = 0.68x.

Problem 4 Got It? A store is offering a 15% discount on all items. Also, employees get a 20% discount (20% off original price(s)). Write a composite function to model taking the 20% discount and then the 15% discount.

Let D(x) = cost after applying the 15% discount, E(x) = cost after applying the 20% employee discount, and x = cost of item(s). Then D(x) = 0.85x and E(x) = 0.80x. (D ◦ E)(x) = 0.68x.

Let D(x) = cost after applying the 15% discount, E(x) = cost after applying the 20% employee discount, and x = cost of item(s). Then D(x) = 0.80x and E(x) = 0.85x. (D ◦ E)(x) = 0.68x.

Problem 4 Got It? Reasoning: In the scenario above, which order of discounts results in a lower cost to the employee?

Taking the 20% discount first results in a lower price.

Taking the 15% discount first results in a lower price.

The total discounts are the same, so it does not matter which discount you take first.

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! You want to buy a sofa that was marked down by $50 before the clearance discount was applied. 

The furniture store may add the 5% sales tax before applying the additional discount, or it may add the sales tax after applying the additional discount. Which way is better for you, the customer?

After

Before

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 the properties of function operations to match equivalent expressions.

h(x)-g(x)

\frac{h(x)}{g(x)}

f(x)+g(x)

(h-g)(x)

(\frac{h}{g})(x)

h(x)\cdot g(x)

(h\cdot g)(x)

(f+g)(x)

Problem 1 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.

Problem 2 Got It?

A

B

C

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 functions f(x) and g(x) and the composite function g(f(x)).
Match equivalent items below.

g(f(x))

x

Domain of f(x)

Range of f(x)

Domain of g(f(x))

(g\circ f)(x)

Problem 3 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: Recall that
(g\circ f)(x)=g(f(x)).
Regardless of how this composition of functions is written, which function is evaluated first?

f(x)

g(x)

Problem 4 Got It? A store is offering a 15% discount on all items. Also, employees get a 20% discount (20% off original price(s)). Write a composite function to model taking the 15% discount and then the 20% discount.

Let D(x) = cost after applying the 15% discount, E(x) = cost after applying the 20% employee discount, and x = cost of item(s). Then D(x) = 0.80x and E(x) = 0.85x. (E ◦ D)(x) = 0.68x.

Let D(x) = cost after applying the 15% discount, E(x) = cost after applying the 20% employee discount, and x = cost of item(s). Then D(x) = 0.85x and E(x) = 0.80x. (E ◦ D)(x) = 0.68x.

Problem 4 Got It? A store is offering a 15% discount on all items. Also, employees get a 20% discount (20% off original price(s)). Write a composite function to model taking the 20% discount and then the 15% discount.

Let D(x) = cost after applying the 15% discount, E(x) = cost after applying the 20% employee discount, and x = cost of item(s). Then D(x) = 0.85x and E(x) = 0.80x. (D ◦ E)(x) = 0.68x.

Let D(x) = cost after applying the 15% discount, E(x) = cost after applying the 20% employee discount, and x = cost of item(s). Then D(x) = 0.80x and E(x) = 0.85x. (D ◦ E)(x) = 0.68x.

Problem 4 Got It? Reasoning: In the scenario above, which order of discounts results in a lower cost to the employee?

Taking the 20% discount first results in a lower price.

Taking the 15% discount first results in a lower price.

The total discounts are the same, so it does not matter which discount you take first.

Problem 1 Got It?

A

B

C

D

Problem 2 Got It?

A

B

C

Problem 3 Got It?

A

B

C

D

Take Note: Recall that
(g\circ f)(x)=g(f(x)).
Regardless of how this composition of functions is written, which function is evaluated first?

f(x)

g(x)

Algebra 2 6-6 Guided Practice: Function Operations

Algebra 2 6-6 Guided Practice: Function Operations

Take Note: What is a composite function ? You may use the canvas to help illustrate your written response.

🧠 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.

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

Take Note: Use the properties of function operations to match equivalent expressions.

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: What is a composite function ? You may use the canvas to help illustrate your written response.

Take Note: Consider functions f(x) and g(x) and the composite function g(f(x)).Match equivalent items below.

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

Problem 4 Got It? A store is offering a 15% discount on all items. Also, employees get a 20% discount (20% off original price(s)). Write a composite function to model taking the 15% discount and then the 20% discount.

Problem 4 Got It? A store is offering a 15% discount on all items. Also, employees get a 20% discount (20% off original price(s)). Write a composite function to model taking the 20% discount and then the 15% discount.

Problem 4 Got It? Reasoning: In the scenario above, which order of discounts results in a lower cost to the employee?

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

Problem 1 Got It?

Problem 2 Got It?

Problem 3 Got It?

Take Note: Recall that(g\circ f)(x)=g(f(x)).Regardless of how this composition of functions is written, which function is evaluated first?

Take Note: What is a composite function ?

You may use the canvas to help illustrate your written response.

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

Take Note: What is a composite function ?

You may use the canvas to help illustrate your written response.

Take Note: Consider functions f(x) and g(x) and the composite function g(f(x)).
Match equivalent items below.

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

Take Note: Recall that
(g\circ f)(x)=g(f(x)).
Regardless of how this composition of functions is written, which function is evaluated first?