Bell Ringer 1-26-17 Since we know visually functions and their inverses are reflections over the line y = x, we should realize that to create an inverse.

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Presentation transcript:

Bell Ringer 1-26-17 Since we know visually functions and their inverses are reflections over the line y = x, we should realize that to create an inverse function, you switch x and y (from transformations in Math II. Based on that, create a table of the inverse of this function. Please use correct function notation for the inverse.

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How do we know if a function has an inverse function? http://www.coolmath.com/algebra/16-inverse-functions/06-one-to-one-01

Examples http://www.coolmath.com/algebra/16-inverse-functions/06-one-to-one-01

Why??? To find an inverse function, you switch the x and y values. Since the x values are the domain of the function, the domain of your function becomes the range of the inverse and the range of the function becomes the domain of the inverse. Sometimes you must restrict the domain to insure the inverse is also a function.

http://www.coolmath.com/algebra/16-inverse-functions/06-one-to-one-01

Classwork Is the relation a function? If so, find the inverse function; restrict the domain if necessary. [(2, 1), (-3, 0), (1, 5)] [(4, 5), (6, 5), (3, 5)] [(-2, 5), (3, 7), (-2, 8)] [(0, -1.1), (2, -3), (1.4, 2), (-3.6, 8)] y = -5x y = 3x – 4 y = x2

homework Is the relation a function? If so, find the inverse function; restrict the domain if necessary. [(3, 4), (4, 3), (6, 5), (5, 6)] [(-2.5, 1), (-1, -1), (0, 1), (-1, 1)] y = 3x y = 7x – 6 y = 2x2 – 3

exit ticket How can you visually determine if two functions are inverses? What test lets you know if a function has an inverse function? What might need to be restricted in a function to insure that its inverse is also a function?