Julia Algebra2

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Author:
delwood
ID:
169393
Filename:
Julia Algebra2
Updated:
2012-10-02 21:39:29
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Algebra
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Algebra 2 cards, must know list
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  1. Vertical line test
    tests if a relation is a function or not. If a vertical line intersects the relations graph in more than one place, then NOT a function
  2. Function
    a process for turning one number (like x) into another (like y). A rule that pairs a bunch of numbers in one set called a Domain into another set called a Range so that no x value repeats. the result is a set of ordered pairs (like x,y)
  3. Domain / Input / Independent variable
    the set of Independent Values or the x's
  4. Range / Output / Dependent variable
    output values from a function or relation or the y's
  5. Increasing function
    its graph rises from left to right. a function increases if f(a) > f(b) for every a > bin the interval.
  6. Decreasing function
    its graph decreased from left to right. a function decreases if f(a) > f(b) for every a < b
  7. Maximum (turning point)
    largest value of function on an interval
  8. Minimum (turning point)
    smallest value of a function on an interval
  9. Vertex
    point where function reaches a max or min, so either a Maximum or Minimum
  10. Continuous graph / function
    Function is continuous at a point (x,y) if it is defined at that point and passes through without a break. Can trace it without lifting pencil.
  11. Discontinuous graph / function
    Cannot be traced without lifting pencil.
  12. Function notation
    f(x) is "f of x" where x is the input value and the f(x) is the output value. apply the rule "f" to the number "x"
  13. Set notation
    to show the solutions to an equation. {(x,y) | y = 3x + 2} or "the set of ordered pairs x,y such that y = 3x + 2"
  14. Value of a function
    The value of f(x) at x or value of y. Find the value by "evaluating the function"
  15. Evaluating a function
    The independent value x is the "placeholder," so plugging in the x-value and getting the y is evaluating the function.
  16. Asymptotes
    A graph never intersects a vertical asymptote but can intersect a horizontal asymptote. Think of a graph with 2 roots (crosses the x-axis) and then approaches the x-axis but never touches it
  17. End behavior
    Directions of the ends of a graph. Think of large |x| on a graph; then what is it doing at the far right or far left.
  18. Multiple representations of functions
    functions can be represented by graphs, tables, function notation like f(x), mapping diagrams, or words. 
  19. Translation / transformation of a function
    An operation that shifts a graph horizontally, vertically or both. Think of y =mx + b and then add 2 to "b" and it shifts the line up by 2 points.
  20. Parent Function
    • A function with its simplest algebraic rule for its shape.
    • This is when you love your Daddy.
  21. Family of functions / types of function
    Functions with common characteristics due to a common algebraic form or similar geometric shape. Think of a function that is shifted up by adding 2 or a parent punction and all its shifts up or sidways.
  22. simplify 2y+xy
    y (2+x)
  23. simplify 3y+xy  
    y(3+x)
  24. 5kkkkkk - 8kkkkkk =  
    -3k to the 6th power
  25. any number to zero power is = 
    1
  26. 12 to the negative 1 is =
    1/2
  27. define irrational number
    any real number that cannot be expressed as a ratio a/b where a and b are integers with b non-zero
  28. reciprocal
    • interchange the numerator and the
    • denominator i.e. invert the
    • fraction
  29. coefficient
    • a number in front of a variable. For example in the
    • expression x2-10x+25 the coefficient of the x2 is 1
  30. absolute value
     the numerical value of a real number without regard to its sign
  31. associative property of multiplication
    • when multiplying three or more real numbers the product is always the same regardless of their grouping
    • (a × b) × c = a × (b × c)
  32. area of a trapezoid
    • A = (b1+b2) h
    •        ________
    •             2

    • =1/2 (b1+b2) h
    • =h/2 (b1+b2)
  33. difference of -5 and 8
    13
  34. area of rectangle with sides 12 and 5
    60
  35. Between what two integers is neg square root of 27
    5 and 6 becasue square of 25 is 5 and 6 squared is 36
  36. graph numbers on number line
    -7/2  |  1.8  |  square root of 6 |  neg sq root of 36  |  pi
    -6______-3.5_______0__1.8___2.45___3.14
  37. 9-6 (18-20)2
    9- 6(-2)= 9-6(4) = -15
  38. 3x2-(4+8x) when x= -2
    3(4)-(-12) = 24
  39. simplify -(y-4x) + 6x - 10y
    • = -y +4x +6x -10y
    • = -11y + 10x
  40. 1/4  (x-2) =8
    • x/4-1/2 = 8
    • x/4 = 8.5
    • x/4 = 17/2
    • x = 17*4/2  =   68/2  = 34
  41. 3(6x-1) = 10x+11
    • 18x-3=10x+11
    • 8x = 14
    • x = 14/8 = 7/4
  42. 2|x-8| + 10 = 20
    • 2x-16 +10 =20
    • 2x = 26
    • x= 13
  43. solve for y:   -3x -9y = 15
    • -9y = 3x-15
    • y = -1/3(x) + 5/3
  44. Solve for C:   F = (9/5) C +32
    • F - 32 = (9/5) C
    • (5/9)F - (5/9)32 = C
  45. Solve for A:  B = (3/5)(A+8)
    • (5/3)B = (A+8)
    • (5/3)B -8 = A
  46. (6/5)(2/9)=
    12/45
  47. 3/11 - 1/2 = 
    6/22 - 11/22 = -5/22
  48. (2/3) / (8/5) =
    (2/3)*(5/8) = 10/24  = 5/12
  49. 2/7 + 3/5 = 
    10/35  + 21/35  =  31/35
  50. 2(13/3) = 
    26/3
  51. (2/7) - 3 = 
    2/7 - 21/7 = -19/21
  52. 4/(7/9) =
    (4/1) / (7/9) = (4*9)/7 = 36/7
  53. (4/5) / 6 =
    (4/5) / (6/1) = 4/30 = 2/15
  54. -8 / (C/3) = 
    (-8/1) / (C/3) = -24 /C 
  55. 4/a - pi/3 = 
    12/3a - 4pi/3a = (12-4pi)/3a 
  56. a/b + c =
    a/b + bc/b = (a+bc) / b
  57. the slope of y = mx + b is
    m
  58. the y-intercept of y=mx+b is
    b
  59. the slope of (A)X + (B)Y = C
    -A/B
  60. the y-Intercept of (A)X + (B)Y = C
    C/B
  61. To find the y-intercept just substitute in _______ for the x  coordinate
    zero

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