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

Posljednje ažuriranje over 3 years ago

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

Posljednje ažuriranje over 3 years ago

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! 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.

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.

Take Note: What is an inverse function?

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

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

F.BF.4.a

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.

F.BF.4.c

F.IF.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.

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

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.

Problem 2 Got It?

F.BF.4.a

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 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.

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

The relations are inverses
The relations are NOT inverses

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.

Instrukcije

Kliknite na karticu Grafikon (Grafikon 1, Grafikon 2 i tako dalje) za svaki grafikon koji trebate nacrtati.
Kliknite na pozadinu grafikona da biste dodali tačku. Dodajte dvije tačke da biste kreirali grafikon. Prevucite tačku ili unesite x i y koordinate da biste uredili njen položaj. Kliknite na tačku da biste je izbrisali.
Nakon što kreirate grafikon, možete označiti kućicu s isprekidanom linijom.

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 are the domain and range of a function and the domain and range of the function's inverse related?

Problem 4 Got It?

F.BF.4.a

F.IF.1

Problem 4 Got It?

F.BF.4.a

Problem 4 Got It?

F.BF.4.a

F.IF.1

Problem 4 Got It?

F.BF.4.a

F.IF.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.

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?

F.BF.4.a

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 a one-to-one function ?

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.

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

F.BF.4.a

Problem 6 Got It?

F.BF.4.a

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.

F.BF.4.a

F.IF.1

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

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

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

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

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

Take Note: What is an inverse function?

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

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

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.

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

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

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

Problem 2 Got It?

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

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.

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

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.

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

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

Problem 4 Got It?

Problem 4 Got It?

Problem 4 Got It?

Problem 4 Got It?

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

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?

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

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

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.

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

Problem 6 Got It?

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.

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

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

Take Note: What is an inverse function?

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

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

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.

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

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

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

Problem 2 Got It?

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

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.

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

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.

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

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

Problem 4 Got It?

Problem 4 Got It?

Problem 4 Got It?

Problem 4 Got It?

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

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?

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

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

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.

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

Problem 6 Got It?

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.

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

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.

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

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.

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.

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?

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.

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

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.

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

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.

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

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.

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.

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?

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.

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

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.

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