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Algebra 2 6-7 Guided Practice: Inverse Relations and Functions

Last updated about 3 years ago

30 questions

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Question 1

1.

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.

Question 2

2.

Solve It! What's wrong with the headline? Why? What is a more appropriate headline?

If you decrease an amount x by 20%, you have 0.2x. If you then increase 0.2x by 20%, you get (0.2x)(1.2) = 0.24x, which is less than the original amount x. The headline states that the mayor's salary was restored, but the mayor's salary will be 76% less than the original salary. A more appropriate headline would be Some of Mayor's Salary Restored. 

If you decrease an amount x by 20%, you have 0.8x. If you then increase 0.8x by 20%, you get (0.8x)(1.2) = 0.96x, which is less than the original amount x. The headline states that the mayor's salary was restored, but the mayor's salary will be 4% less than the original salary. A more appropriate headline would be Most of Mayor's Salary Restored.

Question 3

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.

10

Question 4

4.

Take Note: What is an inverse function?

10

Question 5

5.

Take Note: Create a mapping diagram on the right side of the canvas that represents the inverse of the function shown on the left.

Question 6

6.

Problem 1 Got It? What are the graphs of t and its inverse? Represent both relations as mapping diagrams on the canvas.

Question 7

7.

Problem 1 Got It? Reasoning: Refer to the mapping diagrams you created in the previous item.

Is t a function? Is the inverse of t a function? Explain.

t is a function; the inverse of t is also a function: in both t and its inverse, there is only one y-value for each x-value.  

t is a function; the inverse of t is also a function because there is only one y-value for each x-value. 

t is not a function; the inverse of t is also not a function; in both t and its inverse, there are two y-values for at least one x-value. 

t is a function; the inverse of t is not a function because there are two y-values for one x-value.

Question 8

8.

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

Question 9

9.

Take Note: In general, what is the process for finding the equation for the inverse of a given equation.

10

Question 10

10.

Take Note: Consider finding the inverse of the relation described by y=x^{2}-2.
Place the steps below in the correct order.

Add 2 to each side.
Find the square root of each side.
Switch x and y.

10

Question 11

11.

Problem 2 Got It?

A

B

C

D

Question 12

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.

10

Question 13

13.

Take Note: How can you tell whether two relations are inverses just by looking at their graphs?

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

Question 14

14.

Take Note: Categorize each graph based on whether or not the relations represented are inverses.

The relations are inverses
The relations are NOT inverses

Question 15

15.

Problem 3 Got It? Graph the following 3 lines:

Graph 1: Graph the function y=2x+4.
Graph 2: Graph the inverse of the function.
Graph 3: Graph the function y=x.

Note that the function and its inverse are reflections across the line y = x.

Instructions

Click the graph tab.
Click on the graph background to add a point. Add two points to create a graph. Drag a point or type in x and y coordinates to edit its position. Click on a point to delete it.

Question 16

16.

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

Question 17

17.

Take Note: How are the domain and range of a function and the domain and range of the function's inverse related?

10

Question 18

18.

Problem 4 Got It?

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C

D

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Question 19

19.

Problem 4 Got It?

A

B

C

D

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Question 20

20.

Problem 4 Got It?

A

B

C

D

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Question 21

21.

Problem 4 Got It?

A

B

C

D

Question 22

22.

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

Question 24

24.

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

Question 25

25.

Take Note: What is a one-to-one function ?

10

Question 26

26.

Take Note: What happens when you compose a function and its inverse?

For example, consider:

NOTE: This is NOT a fill-in-the-blank item. You should reply with at least one sentence to answer the question above.

Question 27

27.

Problem 6 Got It? Given g(x) below, find g-1(x).

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Question 28

28.

Problem 6 Got It?

A

B

C

D

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Question 29

29.

Problem 6 Got It?
HINT: You do not actually have to compose these functions. Consider how the composition of any function and its inverse simplifies.

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D

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Question 30

30.

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

Question 23

23.

Problem 5 Got It? The function d, below, relates the distance d, in meters, that an object has fallen to its velocity, v, in meters per second.

What is the inverse of this function?
If a cliff diver falls from a height of 24 meters, what is his velocity in meters per second as he enters the water?

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