One-to-One Functions;

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Presentation transcript:

One-to-One Functions; Section 5.2 One-to-One Functions; Inverse Functions Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

This function is not one-to-one because two different inputs, 55 and 62, have the same output of 38. This function is one-to-one because there are no two distinct inputs that correspond to the same output. Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

For each function, use the graph to determine whether the function is one-to-one. Copyright © 2013 Pearson Education, Inc. All rights reserved

A function that is increasing on an interval I is a one-to-one function in I. A function that is decreasing on an interval I is a one-to-one function on I. Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

The domain of the inverse function is {0.8, 5.8, 6.1, 6.2, 8.3} To find the inverse we interchange the elements of the domain with the elements of the range. The domain of the inverse function is {0.8, 5.8, 6.1, 6.2, 8.3} The range of the inverse function is {Indiana, Washington, South Dakota, North Carolina, Tennessee} Copyright © 2013 Pearson Education, Inc. All rights reserved

State the domain and range of the function and its inverse. Find the inverse of the following one-to-one function: {(-5,1),(3,3),(0,0), (2,-4), (7, -8)} State the domain and range of the function and its inverse. The inverse is found by interchanging the entries in each ordered pair: {(1,-5),(3,3),(0,0), (-4,2), (-8,7)} The domain of the function is {-5, 0, 2, 3, 7} The range of the function is {-8, -4,0 ,1, 3). This is also the domain of the inverse function. The range of the inverse function is {-5, 0, 2, 3, 7} Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

Copyright © 2013 Pearson Education, Inc. All rights reserved

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