HLRGAATPreISM_35799X_05_ch5

# HLRGAATPreISM_35799X_05_ch5 - Chapter 5: Inverse,...

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Chapter 5: Inverse, Exponential, and Logarithmic Functions 5.1: In v erse Functions 1. Different x -values always produce different y -values, therefore yes, it is one-to-one. 2. Different x -values always produce different y -values, therefore yes, it is one-to-one. 3. Choosing 2 and as values for x yields: . Since different values of x produce the same value for the function is not one-to-one. 4. Choosing 2 and as values for x yields: . Since different values of x produce the same value for the function is not one-to-one. 5. Choosing 6 and as values for x yields: . Since different values of x produce the same value for the function is not one-to-one. 6. Choosing 10 and as values for x yields: . Since different values of x produce the same value for the function is not one-to-one. 7. Every horizontal line will intersect the graph at exactly one point, therefore yes, it is one-to-one. 8. Every horizontal line will intersect the graph at exactly one point, therefore yes, it is one-to-one. 9. There are horizontal lines that will intersect the graph at more than one point, therefore it is not one-to-one. 10. A certain horizontal line intersects the whole horizontal graph (more than one point), therefore it is not one-to-one. 11. Every horizontal line will intersect the graph at exactly one point, therefore yes, it is one-to-one. 12. Every horizontal line will intersect the graph at exactly one point, therefore yes, it is one-to-one. 13. Every horizontal line will intersect the graph at exactly one point, therefore yes, it is one-to-one. 14. Every horizontal line will intersect the graph at exactly one point, therefore yes, it is one-to-one. 15. A certain horizontal line intersects the horizontal graph when (more than 1 point), therefore it is not one-to-one. 16. Since different x -values greater than zero all produce the same , it is not one-to-one. 17. Choosing 4 and 0 as values for x yields: . Since different values of x produce the same value for the function is not one-to-one. 18. Choosing 0 and as values for x yields: . Since different values of x produce the same value for the function is not one-to-one. 19. Different x -values always produce different y -values, therefore yes, it is one-to-one. 20. Different x -values always produce different y -values, therefore yes, it is one-to-one. 21. Different x -values always produce different y -values, therefore yes, it is one-to-one. 22. Different x -values always produce different y -values, therefore yes, it is one-to-one. 23. Different x -values always produce different y -values, therefore yes, it is one-to-one. 24. All x -values produce the same , therefore it is not one-to-one. 25. The graph fails the horizontal line test because the end behavior is either or . f 1 x 2 5] 7 f 1 x 2 , f 1 0 2 1 0 1 3 2 2 2 8 17 and f 1 ] 6 2 1 ] 6 1 3 2 2 2 8 17 ] 6 f 1 x 2 , f 1 4 2 5 1 4 2 2 2 2 5 4 and f 1 0 2 5 1 0 2 2 2 2 5 4 f 1 x 2 5 3 x 7 0 f 1 x 2 , f 1 6 2 5 2 100 2 10 2 5 0 and f 1 ] 10 2 5 2 100 2 1 ] 10 2 2 5 0 ] 10 f 1 x 2 , f 1 6 2 5 2 36 2 6 2 5 0 and f 1 ] 6 2 5 2 36 2 1 ] 6 2 2 5 0 ] 6 f 1 x 2 , f 1 2 2 2 2 4 and f 1 ] 2 2 1 ] 2 2 2 4 ] 2 f 1 x 2 , f 1 2 2 5 2 2 5 4 and f 1 ] 2 2 5 1 ] 2 2 2 5 4 ] 2

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26. If the degree is odd and greater than or equal to 3, the graph may have extrema and would then fail the
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## This note was uploaded on 09/24/2011 for the course MATH 1310 taught by Professor Marks during the Spring '08 term at University of Houston.

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HLRGAATPreISM_35799X_05_ch5 - Chapter 5: Inverse,...

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