Pre-Calc midterm

1. How do you find the domain for a square root equation?

   1. set the equation to greater than or equal to zero

2. How do you find the domain for a reciprocal equation?

   1. set the equation so it can't be equal to zero

3. How do you determineIf a function is even, odd, or neither? 

   1. Replace x with (-x), then redistribute the symbols.

4. What is the composition rule?

   1. f(x) of g(x) should equal to X and vice versa, If they do not both equal x then they are not inverses. 

5. What is the first step to determining Zeros, Horizontal Asymptotes, Vertical Asymptotes, and Holes?

   1. Factor the equation. 

6. What is a hole?

   1. When the numerator and denominator has matching factors.

7. What is a zero?

   1. Whatever is remaining on the top of the numerator.

8. What is a vertical Asymptote?

   1. Whatever is remaining on the bottom of the denominator.

9. What is a horizontal asymptote? 

   1. Horizontal aces are dependent on the leading degree of both the numerator and denominator. 

A > B none

A < B y = 0

A = B HA present at y = C/D (the lead coefficients of the denominator and numerator 

8. What is the inverse function of f(x)

   1. f^-1(x)

9. How do you algebraically determine the equation of an inverse function? 

   1. Replace the X value as y, the equal the equation to x and solve for y. 

10. Using the following equations, “-2f-3(x+4))+5” what is the transformation of the first negative sign?

    1. Vertical reflection over the X-axis. 

11. Using the following equations, “-2f-3(x+4))+5” what is the transformation of the value 2?

    1. Vertical dilation over the Y-axis, multiply y values by 2.

12. Using the following equations, “-2f-3(x+4))+5” what is the transformation of the second sign?

    1. Horizontal reflection over the y-axis. 

13. Using the following equations, “-2f-3(x+4))+5” what is the transformation of the value 3?

    1. Horizontal dilation over the x-axis, divide x values by 3. 

14. Using the following equations, “-2f-3(x+4))+5” what is the transformation of +4?

    1. Horizontal translation, 4 units to the left. 

15. Using the following equations, “-2f-3(x+4))+5” what is the transformation of +5?

    1. Vertical translation, 5 units up. 

16. What is the first step to synthetic division? 

    1. Set the zero of the function to not equal 0

17. What is the remainder theorem?

    1. The remainder theorem is when we take a zero of the function and we substitute all X values with said zero. It’s also the same as the factor theorem

18. How can we double check and confirm our remainder theorem?

    1. With synthetic division. 

19. When asked to write a polynomial function of minimum degree in standard form with real coefficients whose zeros include 2 and 3+i and has a y-intercept of 100, what must we remember? What and how do we muliplyt all our zeros 

    1. Our zeros are (x - 2)(x - (3 + i))(x - (3 - i))

20. How to determine the number of complex zeros the polynomial function has and determine a list of potential real rational zeros of a polynomial.

    1. The highest degree of a polynomial is the indicator for how many complex zeros there are in a function, and P/Q is how you determine the list of potential real rational zeros of the polynomial. 

21. In multiplicity, What does an even and odd multiplicity do on a graph 

    1. And even multiplicity will bounce off the x-axis, while an odd multiplicity will cross through the x-axis. 

22. What can you use to find all the complex zeros?

    1. Quadratic formula and factor by grouping 

23. How to simplify complex expressions 

    1. Multiply like values and stop there 

24. What is the formula for the exponential function?

    1. f(x) = AB^x

25. How to determine the formula of an exponential function with a table

    1. First, A should be whatever value f(x) is when x is 0, 

Next, to find B is A(f(x)) B = (when x is 1) then solve.  

26. Describe the identity function

    1. Diagonal line through origin

27. Describe the squaring function

    1. Parabola (U-shape), Symmetric around the Y axis

28. Describe the cubing function

    1. S-shaped curve, passes through origin

29. Describe the absolute value function

    1. “V” shape

30. Describe the Exponential function

    1. Rapid growth 

31. Describe the reciprocal function

    1. Hyperbola with vertical and horizontal Asymptotes

32. Describe the square root function

    1. Increasing curve starting at origin 

33. Describe the sine function 

    1. Squiggly line that crosses through the origin

34. Describe the cosine function

    1. Squiggly line that is symmetric along the y-axis 

35. Describe the logistic function

    1. A very stretched out S-shaped curve.

36. Describe the natural function

    1. Slow, increasing curve with vertical asymptote at x=0.

37. Describe the greatest integer function

    1. A staircase 

38. What function is this: f(x) = x

    1. Identity function

39. What function is this: f(x) = |x|

    1. Absolute value function

40. What function is this: f(x) = √x

    1. Square root function

41. What function is this: f(x) = x²

    1. Squaring functions

42. What function is this: f(x) = 1/x

    1. Reciprocal function

43. What function is this: f(x) = sin(x)

    1. Sine function

44. What function is this: f(x) = e^x

    1. Exponential function

45. What function is this: f(x) = 1 / 1+e^-x 

    1. Logistic function

46. What function is this: f(x) = x³

    1. Cubing function

47. What function is this: f(x) = cos(x)

    1. Cosine function

48. What function is this: f(x) = int(x)

    1. Greatest integer function

49. What function is this: f(x) = ln(x)

    1. Natural log function 

50. Is the identity function bounded

    1. Unbounded

51. Is the squaring function bounded

    1. Bounded below

52. Is the cubing function bounded

    1. Unbounded 

53. Is the absolute value function bounded 

    1. Bounded below

54. Is the exponential function bounded

    1. Bounded below

55. Is the reciprocal function bounded

    1. Unbounded

56. Is the square root function bounded

    1. Bounded below

57. Is the Sine function bounded

    1. Bounded

58. Is the cosine function bounded

    1. Bounded

59. Is the logistic function bounded

    1. Bounded

60. Is the natural log function bounded

    1. Bounded above

61. Is the greatest integer function bounded

    1. Unbounded 

62. What is the exponential function equation 

    1. f(x) = AB^x

63. What is the first step to finding an exponential function?

    1. Find the value of A when x is 0

64. What is the Second step to finding an exponential function?

    1. The equation should equal whatever when x is is 1

65. What is the compound interest formula 

    1. P(1 + R/n)^(n)(t)

    2. The more you compound the larger n gets

66. What is a>o & k>o

    1. growth

67. What is a>o & k<o

    1. decay

68. How to solve logistic functions?

    1. CAB

69. What is the CAB equation?

    1. C / 1+AB^x
       

Never forget the Switch aroooo

70. What is the equivalent of y = b^x

    1. y^-1 = log b^x

71. How to find inverse functions from log? Ex: logb 1 = 0

    1. Arrow from b to 0 and arrow from 0 to 1

72. log 100 = ?

    1. log 10 100 base 10 is ignorable. 

73. What does ln e√e = x equal to

    1. switcharoo e^x = √e

Square root can be ½ 

74. What does e ^{ln 4} = z equal to??

    1. log e Z = ln 4

75. How else can log e Z = ln 4 be written?

    1. ln Z = ln 4 Z = 4