PRECAL REVIEW DAY 11/14/17

Transcription

1 PRECAL REVIEW DAY 11/14/17

2 COPY THE FOLLOWING INTO JOURNAL 1 of 3 Transformations of logs Vertical Transformation Horizontal Transformation g x = log b x + c g x = log b x c g x = log b (x + c) g x = log b (x c) Shift graph up Shift graph down Shift graph left Shift graph right Reflection g x = log b x g x = log b ( x) Reflect about x-axis Reflects about y-axis Vertical Stretching or Shrinking g x = c log b x Vertically stretches if c > 1 Vertically shrinks if 0 < c < 1 Horizontal Stretching or Shrinking g x = log b cx Horizontally shrinks if c > 1 Horizontally stretches if 0 < c < 1

3 COPY THE FOLLOWING INTO JOURNAL 2 of 3 Transformations of exponents Vertical Translation g x = c x + k Shift graph up if k > 0 Shift graph down if k < 0 Horizontal Translation g x = c x+k Shift graph left if k > 0 Shift graph right if k < 0 Reflection g x = c x g x = c x Reflect about x-axis Reflects about y-axis Vertical Stretching or Shrinking g x = kc x Vertically stretches about x-axis by a factor of k Horizontal Stretching or Shrinking g x = c kx Horizontally stretch about y-axis by a factor 1 k

4 COPY THE FOLLOWING INTO JOURNAL 3 of 3 Important Concepts/Formulas IF log b x = y THEN b y = x ln = natural log e = natural base Compound Interest Formula A = P(1 + r n )nt Continuous Compound Interest Formula A = Pe rt Exponential Growth/Decay N = N 0 (1 + r) t Continuous Exponential Growth/Decay N = N 0 e kt

5 Evaluate the expression log

6 ANSWER 4

7 Solve this equation 25 3x+2 = 125

8 ANSWER 1 6

9 Evaluate this equation log 4 16

10 ANSWER 2

11 Condense the expression 2 log 4 m + 6 log 4 n 3(log log 4 j)

12 ANSWER log 4 m 2 n 6 (3j) 3

13 ANSWER log 4 m 2 n 6 27j 3

14 Word Problem If P = $250, r = 7%, and t = 6 years, what is the investment if the interest is compounded daily?

15 ANSWER $380.48

16 Expand this expression log 5 x 2 a 7 b *Hint exponent fractions are written in what form?

17 ANSWER 2log 5 x + 7 log 5 a log 5 b

18 Evaluate this equation e ln 12

19 ANSWER 12

20 Solve this equation 3 x+3 = 27 x 2

21 ANSWER 9 2

22 Condense the expression 3 log 3 x 2 log 3 y

23 ANSWER log 3 x 3 y 2

24 Word Problem If P = $250, r = 7%, and t = 6 years, what is the investment if the interest is compounded annually?

25 ANSWER $375.18

26 Solve this equation log 6 x + log 6 (x 5) = 2

27 ANSWER 9

28 Expand this expression log 3 9x 3 y 3 z 6

29 ANSWER log 3 x + 3 log 3 y + 6 log 3 z

30 Word Problem If P = $250, r = 7%, and t = 6 years, what is the investment if the interest is compounded continuously?

31 ANSWER $380.49

32 Evaluate the expression log 10 12

33 ANSWER 12

34 Condense the expression 5 ln(x + 3) + 3 ln 2x 4 ln(x 1)

35 ANSWER ln 8x3 (x + 3) 5 (x 1) 4

36 Solve this equation e 2x 8e x + 15 = 0 *Hint what do you do to quadratic equations

37 ANSWER ln 3 or ln 5

38 Evaluate this equation log 25 5

39 ANSWER 1 2

40 Solve this equation 3 x+8 = 9 2x

41 ANSWER 8 3

42 Transformation If f x = 5 x. Then if g x = 5 x 2. What is the transformation?

43 ANSWER The graph is translated 2 units to the right

44 Evaluate this equation ln e 11

45 ANSWER 11

46 Evaluate the expression 9 log 9 5.3

47 ANSWER 5.3

48 Word Problem If P = $250, r = 7%, and t = 6 years, what is the investment if the interest is compounded quarterly?

49 ANSWER $379.11

50 Transformation If f x = 4 x. Then if g x = 4 x. What is the transformation?

51 ANSWER The graph is translated over the y-axis

52 Evaluate this equation 3 log 3 9

53 ANSWER 9

54 Solve this equation log 2 x + log 2 3 = log 2 18

55 ANSWER 6

56 Expand this expression log 6 36xy 2

57 ANSWER 2 + log 6 x + 2 log 6 y

58 Expand this expression ln e x 2 y 3 z

59 ANSWER 1 2 ln x 3 ln x ln z

60 Evaluate this equation log 2 32

61 ANSWER 5

62 Solve this equation e x 4e x = 0

63 ANSWER ln 2

64 Transformation If f x = 5 x. Then if g x = 5 x. What is the transformation?

65 ANSWER The graph is translated over the x-axis

66 Word Problem You invest $1500 in an account with an interest rate of 8% for 12 years, making no other deposits or withdrawals. What will be your account balance if the interest is compounded monthly?

67 ANSWER $

68 Solve this equation log 2 (x 1) + 1 = log 2 x + 3

69 ANSWER 5

70 Word Problem If P = $250, r = 7%, and t = 6 years, what is the investment if the interest is compounded monthly?

71 ANSWER $380.03

72 Evaluate this equation log 13 1

73 ANSWER 0

74 Condense the expression 1 3 log 2 a log 2 (b + 1)

75 ANSWER log 2 3 a(b + 1)