659 6.6 Graphs of the Secant and Cosecant Functions I 1. The least positive value k for which x = k is a vertical asymptote for y = sec x 2. The least positive value k for which x = k is a vertical asymptote for y = csc x 3. The least positive value that is in the range of y = sec x 4. The greatest negative value that is in the range of y = csc x 5. The greatest negative value of x for which sec x = -1 6. The least positive value of x for which csc x = -1 6.6 Exercises II A. p 2 B. p C. -p D. 1 E. 3p 2 F. -1 CONCEPT PREVIEW Match each description in Column I with the correct value in Column II. Refer to the basic graphs as needed. Graph each function over a one-period interval. See Examples 1 and 2. 11. y = 3 sec 1 4 x 12. y = -2 sec 1 2 x 13. y = - 1 2 csc ax + p 2b 14. y = 1 2 csc ax - p 2b 15. y = csc ax - p 4b 16. y = sec ax + 3p 4 b 17. y = sec ax + p 4b 18. y = csc ax + p 3b 19. y = csc a 1 2 x - p 4b 20. y = sec a 1 2 x + p 3b 21. y = 1 2 csc a2x + p 2b 22. y = - 1 2 sec a4x - p 2b 23. y = 2 + 3 sec12x - p2 24. y = 1 - 2 csc ax + p 2b 25. y = 1 - 1 2 csc ax - 3p 4 b 26. y = 2 + 1 4 sec a 1 2 x - pb Concept Check Match each function with its graph in choices A – D. 7. y = -csc x 8. y = -sec x 9. y = sec ax - p 2b 10. y = csc ax + p 2b A. 3p 2 x 0 1 – –1 p 2 p 2 y B. x y 0 1 –1 p 2p C. x y 0 1 – –1 p 2 p 2 D. x 0 1 –p p y –1
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