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

Last updated almost 3 years ago
30 questions
3

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

5

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

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

10

Take Note: What is an inverse function?

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

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

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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.

3

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

10

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

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

  1. Switch x and y.
  2. Add 2 to each side.
  3. Find the square root of each side.
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Problem 2 Got It?

3

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

10

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.

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

  • The relations are inverses
  • The relations are NOT inverses
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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.

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

10

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

10

Problem 4 Got It?

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Problem 4 Got It?

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Problem 4 Got It?

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Problem 4 Got It?

3

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

10

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?

3

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

10

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

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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.

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

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Problem 6 Got It?

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