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Review Warm-up: Find the Domain of Each Function

Review Warm-up: Find the Domain of Each Function . Text search:3.7 pp.265 . What is a one-to-one function? How can you tell if a function is one-to-one by examining the graph? Create 2 one-to-one functions and 2 functions that are not one-to-one functions.

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Review Warm-up: Find the Domain of Each Function

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  1. Review Warm-up: Find the Domain of Each Function

  2. Text search:3.7 pp.265 • What is a one-to-one function? How can you tell if a function is one-to-one by examining the graph? Create 2 one-to-one functions and 2 functions that are not one-to-one functions.

  3. Find a function that “ “undoes”each equation

  4. OK, but is there an easier way than trial and error • Yes, switch x and y and solve for y • Try it for the examples you just figured out

  5. Exploring inverse functions (on big paper) • For your function A,B,C,D,E or F • State the inverse function, label it as • Create a table of values for the function and its inverse. Be mindful of what numbers to use as inputs to the inverse function • Graph the function and its inverse on the same set of axes • Compose the function and its inverse in both orders

  6. Conclusions: An inverse function “undoes” the original function • Its ordered pairs are reversed • The graph of a function and its inverse are reflections over the line y=x • The composition of the two functions yields x

  7. Hmmm… • How can we restrict the domain of so that it is a one-to-one function?

  8. Inverse Functions in a Problem Context • 3.7 #76 , Toricelli’s Law • A tank holds 100 gallons of water, which drains from a leak at the bottom, causing the tank to empty in 40 minutes. Toricelli’s Law gives the volume of water remaining in the tank after x minutes as . • Find , What does it represent? • Find , What does your answer represent?

  9. Homework Preview:

  10. Homework Preview: • Find the inverse function for

  11. Homework Preview • Use Inverse Function Property to verify that f and g are inverses of eachother (composition)

  12. Reminders . . . • Project due Tuesday • Classwork 3.7 #70,72,75,83 (we did 76) • Homework 3.7 #21-40

  13. Homework Quiz • A. • B.Find the inverse of g(x): • C. Use composition to verify that f and g are inverses

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