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Exponentials and  logs exact values properties and domain and range
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Exponentials and logs exact values properties and domain and range

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Transcript

  • 1. e-2 =
  • 2. Answer 1 = 2 e
  • 3. ln(3x5) =
  • 4. Answer=ln3 + lnx5=ln3 + 5lnx
  • 5. eln3=
  • 6. Answer =3
  • 7.  xy 5 ln  6 =   
  • 8. Answer= ln x + 5 ln y − ln 6
  • 9. For y=lnx, can x = 0?
  • 10. Answer No!Domain of natural log is (0, ∞)
  • 11. For y=2x, can x be 0?
  • 12. Answer Yes! Domain of exponential is (−∞, ∞) any # to the 0 power is 1(0,1) point on parent graph
  • 13. For y=2x, can y be negative?
  • 14. Answer No!Range of exponential is (0, ∞)
  • 15. ln0 =
  • 16. Answer= undefined
  • 17. lne2 =
  • 18. Answerlne2 = 2lne = 2(1) = 2
  • 19. ln1 =
  • 20. Answer =0
  • 21. ln(-2) =
  • 22. Answer= undefined
  • 23. e0 =
  • 24. Answer =1
  • 25. For y=2x, can x be negative?
  • 26. Answer Yes!Domain of exponential is (−∞, ∞)
  • 27. For y=2x, can y = 0?
  • 28. Answer No! Range of exponential is (0, ∞)HA at y=0 (for parent graph)
  • 29. For y=lnx, can x be negative?
  • 30. Answer No!Domain of natural log is (0, ∞)
  • 31. For y=lnx, can y = 0?
  • 32. Answer Yes! Range of natural log is (−∞, ∞) (inverse of exponential)(1,0) is a point on the parent graph
  • 33. Does ln(x +1) = 2lnx2 + ln1 = 2lnx + 0 ?
  • 34. Answer NO!It is the natural log of that quantity.