Understanding Inverse Functions Concepts

This video introduces inverse functions, explaining that they swap the domain and range of the original function. Using an escalator analogy, the video illustrates the concept of inverse functions. It then demonstrates how to create inverse tables by swapping x and y values and graphing these points. The video also covers how to verify the accuracy of inverse graphs by checking for symmetry. Finally, it discusses the vertical line test to determine if an inverse is a function, noting that not all inverses are functions.

What is an inverse function?

• A function that doubles the input values

• A function that adds a constant to the input values

• A function that swaps its domain and range

• A function that squares the input values

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CCSS.8.F.A.1

CCSS.HSF.IF.A.1

In the escalator analogy, what does the inverse function represent?

• Staying at the top

• Staying at the bottom

• Going from the top to the bottom

• Going from the bottom to the top

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CCSS.HSF-BF.B.4C

How do you create an inverse table?

• By multiplying all values by 2

• By swapping the x and y values

• By adding 1 to all x values

• By subtracting 1 from all y values

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CCSS.HSF-BF.B.4C

What is the inverse of the point (2, 3) in the table?

• (3, -2)

• (-2, 3)

• (2, -3)

• (3, 2)

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CCSS.HSF-BF.B.4C

Which of the following points is correctly swapped to form an inverse?

• (1, 0) to (0, 1)

• (0, -1) to (-1, 0)

• (-2, 3) to (3, -2)

• All of the above

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CCSS.HSF-BF.B.4C

How can you visually check if you have graphed the inverse function correctly?

• By drawing a vertical line

• By drawing a circle

• By drawing a horizontal line

• By drawing a diagonal line

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CCSS.HSF-IF.C.7A

What should you notice when you tilt your head to the side after drawing the diagonal line?

• The graph should look like a triangle

• The graph should look like a square

• The upper and lower parts should be mirror images

• The graph should look like a circle

What test can you use to determine if the inverse of a function is itself a function?

• Mirror image test

• Vertical line test

• Horizontal line test

• Diagonal line test

What does it mean if a vertical line intersects the inverse graph multiple times?

• The inverse is a function

• The inverse is not a function

• The graph is not drawn correctly

• The original function is incorrect

Can the inverse of a function sometimes not be a function itself?

• No, only if the original function is incorrect

• Yes, sometimes

• No, never

• Yes, always