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Inverse Functions Lesson Warm-Up and Talking Points Included

Inverse Functions Lesson Warm-Up and Talking Points Included. Algebra I. Warm-Up for Inverse Function Lesson REVIEW 1. A relation is a set of _______________ ___________.

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Inverse Functions Lesson Warm-Up and Talking Points Included

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  1. Inverse FunctionsLessonWarm-Up and Talking Points Included Algebra I

  2. Warm-Up for Inverse Function Lesson REVIEW 1. A relation is a set of _______________ ___________. 2. A function is a special relation where there is ________________________________ _______________________________________________________________________. 3. Create ordered pairs for the function displayed in the mapping. 4. Inverse Operations UNDO one another. State the inverse operation. a. Addition b. Subtraction c. Multiplication d. Division e. Squaring -6 -4 -1 0 6 -2 0 3 4 6 Talk about a regular function is The inverse function is Really you are just switching your input and output, or x and y values. Show ordered pairs of

  3. If you watched the Kahn Academy video, he talked through solving for the opposite variable, solving for x (which is highly unusual with a linear function … we always solve for y … think of y=mx+b, etc.) Then he showed swapping out the y for the x at the end. That’s all fine and good, but I actually find it easier to swap the variables in the first place and solve for y (like we are used to doing). If you understand that INVERSES undo and go backwards … (instead of DR … RD; instead of xy, yx) swap them right up front!

  4. Suppose you are given the following directions: • From home, go north on Rt 23 for 5 miles • Turn east (right) onto Orchard Street • Go to the 3rd traffic light and turn north (left) onto Avon Drive • Tracy’s house is the 5th house on the right. • If you start from Tracy’s house, write down the directions to get home. • How did you come up with the directions to get home from Tracy’s?

  5. Suppose you are given the following algorithm: • Starting with a number, add 5 to it • Divide the result by 3 • Subtract 4 from that quantity • Double your result • The final result is 10. Working backwards knowing this result, • find the original number. Show your work.

  6. Suppose you are given the following algorithm: • Starting with a number, add 5 to it • Divide the result by 3 • Subtract 4 from that quantity • Double your result • The final result is 10. Working backwards knowing this result, • find the original number. Show your work. • Write a function f(x), which when given a number x (the original number) will model the operations given above. • Write a function g(x), which when given a number x (the final result), will model the backward algorithm that you came up with above.

  7. On the Kahn Academy video, you were shown how a function and it’s inverse reflect over the line y=x.. This is a great example. The green line is . The red line is .

  8. On the Kahn Academy video, you were shown how a function and it’s inverse reflect over the line y=x.. This is a CRAZY example. The green line is . The red line is

  9. Inverse Functions • A function and its inverse function can be described as the "DO" and the "UNDO" functions.  • A function takes a starting value, performs some operation on this value, and creates an output answer.  • The inverse function takes the output answer, performs some operation on it, and arrives back at the original function's starting value. • How to create an inverse function: Example #1 • 1. Change f(x) to y • 2. Switch x and y • 3. Solve for y • 4. Use inverse notation f -1(x) The graph of an inverse function switches the x and y values completely. Function graphs (x, y) Inverse Function graphs (y, x) It’s graph is reflected over the line y = x.

  10. Find the algebraic inverse and graph the function and inverse on the same coordinate plane. 2. 3.

  11. Is the inverse a function? If the inverse is not a function, how can you restrict the domain of the original function so that the inverse is also a function? Is the inverse a function? If the inverse is not a function, how can you restrict the domain of the original function so that the inverse is also a function?

  12. Go to Kahn Academy and watch the video for Inverse Functions Example 2 https://www.khanacademy.org/math/algebra/algebra-functions/function_inverses/v/function-inverses-example-2 Find if

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