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Chapter 4: Graphing Functions

Chapter 4: Graphing Functions. 4.4 Other Trig Functions 4.5 Finding an Equation from its Graph. Review of Sine and Cosine. Domain: Range: y -intercept: Amplitude: Period:. 4 3 2 1 - 1 - 2 - 3 - 4.

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Chapter 4: Graphing Functions

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  1. Chapter 4:Graphing Functions 4.4 Other Trig Functions 4.5 Finding an Equation from its Graph

  2. Review of Sine and Cosine Domain: Range: y-intercept: Amplitude: Period: 4 3 2 1 -1 - 2 - 3 - 4 -4p -3p -2p-pp 2p 3p 4p

  3. Review of Sine and Cosine Domain: Range: y-intercept: Amplitude: Period: 4 3 2 1 -1 - 2 - 3 - 4 -4p -3p -2p-pp 2p 3p 4p

  4. Review of Sine and Cosine Domain: Range: y-intercept: Amplitude: Period: 4 3 2 1 -1 - 2 - 3 - 4 -4p -3p -2p-pp 2p 3p 4p

  5. Review of Sine and Cosine 4 3 2 1 -1 - 2 - 3 - 4 -4p -3p -2p-pp 2p 3p 4p

  6. Review of Sine and Cosine 4 3 2 1 -1 - 2 - 3 - 4 -4p -3p -2p-pp 2p 3p 4p

  7. Review of Sine and Cosine 4 3 2 1 -1 - 2 - 3 - 4 -4p -3p -2p-pp 2p 3p 4p

  8. Review of Sine and Cosine Phase Shift Period 4 3 2 1 -1 - 2 - 3 - 4 -4p -3p -2p-pp 2p 3p 4p

  9. Review of Sine and Cosine Phase Shift Period 4 3 2 1 -1 - 2 - 3 - 4 -4p -3p -2p-pp 2p 3p 4p

  10. Refer to 2nd graph. COSECANT & SECANT GRAPHS Think: 4 3 2 1 -1 - 2 - 3 - 4 -4p -3p -2p-pp 2p 3p 4p

  11. Refer to 1st graph. COSECANT & SECANT GRAPHS Think: 4 3 2 1 -1 - 2 - 3 - 4 -4p -3p -2p-pp 2p 3p 4p

  12. Refer to 3rd graph. COSECANT & SECANT GRAPHS Think: 4 3 2 1 -1 - 2 - 3 - 4 -4p -3p -2p-pp 2p 3p 4p

  13. TANGENT & COTANGENT GRAPHS Domain: Range: y-intercept: Period: 4 3 2 1 -1 - 2 - 3 - 4 -4p -3p -2p-pp 2p 3p 4p Asymptotes:

  14. TANGENT & COTANGENT GRAPHS Domain: Range: y-int: Period: Asymptotes SHIFT Asymptotes: 4 3 2 1 -1 - 2 - 3 - 4 ORIGINAL ASYMPTOTE -4p -3p -2p-pp 2p 3p 4p

  15. TANGENT & COTANGENT GRAPHS Phase Shift Period 4 3 2 1 -1 - 2 - 3 - 4 -4p -3p -2p-pp 2p 3p 4p

  16. TANGENT & COTANGENT GRAPHS Phase Shift Period 4 3 2 1 -1 - 2 - 3 - 4 -4p -3p -2p-pp 2p 3p 4p

  17. TANGENT & COTANGENT GRAPHS Period then reflect across x-axis 4 3 2 1 -1 - 2 - 3 - 4 -4p -3p -2p-pp 2p 3p 4p

  18. Which equation matches the graph? A C B D 4 3 2 1 -1 - 2 - 3 - 4 -4p -3p -2p-pp 2p 3p 4p

  19. Which equation matches the graph? A C B D 4 3 2 1 -1 - 2 - 3 - 4 -4p -3p -2p-pp 2p 3p 4p

  20. Which equation matches the graph? A C B D 4 3 2 1 -1 - 2 - 3 - 4 -4p -3p -2p-pp 2p 3p 4p

  21. Write the equation for the graph. 0 0 1 1 4 tan 4 3 2 1 -1 - 2 - 3 - 4 -4p -3p -2p-pp 2p 3p 4p

  22. Write the equation for the graph. -p 2 1 1 1 cot 4 3 2 1 -1 - 2 - 3 - 4 -4p -3p -2p-pp 2p 3p 4p

  23. Which equation matches the graph? A C B D 4 3 2 1 -1 - 2 - 3 - 4 -4p -3p -2p-pp 2p 3p 4p

  24. Which equation matches the graph? A C B D 4 3 2 1 -1 - 2 - 3 - 4 -4p -3p -2p-pp 2p 3p 4p

  25. Write the equation for the graph. 4 3 2 1 -1 - 2 - 3 - 4 -4p -3p -2p-pp 2p 3p 4p

  26. Write the equation for the graph. 4 3 2 1 -1 - 2 - 3 - 4 -4p -3p -2p-pp 2p 3p 4p

  27. Amplitude: A A < 0 reflect x Period: B < 0 reflect y 2p ___ B f (x)= A sin[B(x + C )] + D f (x)= Acos[B(x + C )] + D Phase shift: Displacement: D -C D > 0 up D < 0 down C > 0 left C < 0 right

  28. Amplitude: A A < 0 reflect x Period: B < 0 reflect y 2p ___ B f (x)= Acsc[B(x + C )] + D f (x)= A sec[B(x + C )] + D Phase shift: Displacement: D -C D > 0 up D < 0 down C > 0 left C < 0 right

  29. A < 0 reflect x Period: B < 0 reflect y p ___ B f (x)= A tan[B(x + C )] + D f (x)= A cot[B(x + C )] + D Phase shift: Displacement: D -C D > 0 up D < 0 down C > 0 left C < 0 right

  30. What about asymptote equations? [B(x + C )] f (x)= A trig[B(x + C )] + D = parent asymptote Parent Asymptote secant & tangent : cosecant & cotangent :

  31. What about asymptote equations? [B(x + C )] f (x)= A trig[B(x + C )] + D = parent asymptote Parent Asymptote secant & tangent : cosecant & cotangent :

  32. Refer to 4th graph. asymptote: 4 3 2 1 -1 - 2 - 3 - 4 -4p -3p -2p-pp 2p 3p 4p

  33. Refer to 7th graph. asymptote: 4 3 2 1 -1 - 2 - 3 - 4 -4p -3p -2p-pp 2p 3p 4p

  34. Refer to 1st graph. asymptote: 4 3 2 1 -1 - 2 - 3 - 4 -4p -3p -2p-pp 2p 3p 4p

  35. Refer to 5th graph. asymptote: 4 3 2 1 -1 - 2 - 3 - 4 -4p -3p -2p-pp 2p 3p 4p

  36. Refer to 3rd graph. asymptote: 4 3 2 1 -1 - 2 - 3 - 4 -4p -3p -2p-pp 2p 3p 4p

  37. Refer to 6th graph. asymptote: 4 3 2 1 -1 - 2 - 3 - 4 -4p -3p -2p-pp 2p 3p 4p

  38. Refer to 2nd graph. asymptote: 4 3 2 1 -1 - 2 - 3 - 4 -4p -3p -2p-pp 2p 3p 4p

  39. Write the asymptote equation for the trigonometric function.

  40. Write the asymptote equation for the trigonometric function.

  41. THE END

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