651 6.5 Graphs of the Tangent and Cotangent Functions Graph each function over a one-period interval. See Examples 1 – 3. 13. y = tan 4 x 14. y = tan 1 2 x 15. y = 2 tan x 16. y = 2 cot x 17. y = 2 tan 1 4 x 18. y = 1 2 cot x 19. y = cot 3x 20. y = -cot 1 2 x 21. y = -2 tan 1 4 x 22. y = 3 tan 1 2 x 23. y = 1 2 cot 4 x 24. y = - 1 2 cot 2 x A. x y 0 p B. x y 0 4 –p 3p 4 C. x y 0 –p 2 p 2 D. x y 0 p 4 5p 4 E. x y 0 p 4 3p 4 – F. x y 0 4 –p 3p 4 Concept Check Match each function with its graph in choices A – F. 7. y = -tan x 8. y = -cot x 9. y = tan ax - p 4b 10. y = cot ax - p 4b 11. y = cot ax + p 4b 12. y = tan ax + p 4b Graph each function over a two-period interval. See Examples 4 and 5. 25. y = tan12 x - p2 26. y = tan a x 2 + pb 27. y = cot a3x + p 4b 28. y = cot a2 x - 3p 2 b 29. y = 1 + tan x 30. y = 1 - tan x 31. y = 1 - cot x 32. y = -2 - cot x 4. Between any two successive vertical asymptotes, the graph of y = cot x . (increases / decreases) 5. The negative value k with the greatest value for which x = k is a vertical asymptote of the graph of y = tan x is . 6. The negative value k with the greatest value for which x = k is a vertical asymptote of the graph of y = cot x is .
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