College Algebra

  1. Name the three terms for the domain
    x-axis / input / interval
  2. Name the two terms for range
    y-axis / output
  3. Define function
    Relation in which each input has one and only one output
  4. Determine if the domain and range of the relation and explain why.

    [(-2,-1), (1,-6), (5,-1), (8,-9), (11,8)]
    Image Upload 1

    No repeating x values
  5. Determine the domain and range of the relation.

    [(-3,-4), (1,6), (-9, -8), (4, -6), (-1, 9)]
    Domain (x): (-3, 1, -9, 4, -1)

    Range (y):   (-4, 6, -8, -6, 9)
  6. Tell whether the relation is a function and explain why.

    [(7,7), (1,7), (6,1), (11,6), (1,-8)]
    Image Upload 2


    Not a function, cannot have two x values
  7. What is a "Vertical Line Test"?
    If a vertical line intersects more than once on the graph, then it is not a function.
  8. What sign do you use for the graph notation below?

    ∞, 5
    [∞, 5)
  9. What order do you notate graph points?
    (lowest, highest)
  10. What does it mean if you have a non-function from a vertical line test?
    If it intersects, then you have two x values.
  11. What does the symbol below mean?

    union
  12. When combining two domains below, what would be the long and simplified (final) answer?

    ∞, 0 & 0, ∞
    Long answer: [∞,0) U (0,∞] 

    Simplified: [∞,∞]
  13. What does f(x) equal?
    range / y-axis
  14. Find f(-x) when f(x) = x^2 - 2x - 2
    (-x)^2 - 2(-x) - 2

    x^2 + 2x -2
  15. Simplify (-x)^2
    x^2
  16. Find f(-4) when f(x) = x^2 - 2x - 2
    (-4)^2 - 2(-4) - 2

    16 + 8 - 2 = 22
  17. When determining where a function might be increasing/decreasing/constant, how do you use the x- and y-values of the graph?
    Refer to y-axis from left to right
  18. What is the slope function?
    • y2-y1
    • m = _____
    •        x2-x1
  19. What is the slope intercept function?
    y = mx + b
  20. What is the point-slope function?
    y - y = m(x - x)
  21. What is the general or standard function?
    ax + by = c
  22. What axis is the horizontal line?
    y
  23. What axis is the vertical line?
    x-axis
  24. What is a common value with parallel lines?
    It has the same slope
  25. What is the sign for slope?
    m
  26. What does the sign below mean?

    m
    slope
  27. What slopes have negative reciprocals?
    Perpendicular lines
  28. How do you map the slope function on a graph?
    rise/run from y - axis point
  29. Define the slope below.

    4/0
    undefined
  30. If the line is undefined, what direction is the line going?
    vertical
  31. What is the point-slope form of the equation of the line?

    Slope = 6, passing through (-5,9)
    y - 9 = 6(x - (-5))
  32. What is the slope-intercept form of the equation of the line of the point-slope form below?

    y - 9 = 6(x-(-5))
    y = 6x + 39
  33. If a line rises from left to right, the line has _______slope.
    positive
  34. A line that falls from left to right has a _________ slope
    negative
  35. The slope of a horizontal line is _____
    0
  36. The slope of a vertical line is _________
    Undefined
  37. The equation y=3 is a
    horizontal line
  38. The graph of the equation x=3 is a
    vertical line
  39. f(x)=?
    y
  40. What is the vertical line test?
    If a vertical line passes through an x value twice on the graph
  41. Find  F(-4) when f(x) = x^2 - 2x - 2
    (-4)^2 - 2(-4) - 2

    16+8+2 = 22
  42. Find f(0) when f(x) = x^2 + 5 -4
    0^2 + 5(0) - 4 = -4
  43. Find F(-x) when f(x) = x^2 - 2x - 2
    (-x)^2 - 2(-x) - 2

    x^2 + 2x - 2
  44. If you are asked f(3) = ? . What steps are there to find correct point on the graph?
    refer to x-axis to find 3 first and find corresponding y-axis point below or above the x-axis
  45. If you are asked f(x)=4 what steps to find the correct point on the graph?
    First, find 4 on the y-axis and then find corresponding x-axis point to the left or right of the y-axis
  46. Find the slope for the points and indicate whether the line through the points rise, fall, is horizontal or vertical. (2,4) and (3,6)
    2

    Line rises from left to right
  47. Find the slope for the points and indicate whether the line through the points rise, fall, is horizontal or vertical. (-7,5) and (-7,9)
    slope is undefined

    The line is vertical
  48. If is a line is undefined, it is what?
    vertical
  49. If a line is vertical, it is what?
    undefined
  50. Write the point-slope from of the line satisfying the given conditions. Then use the point-slope form of the equation to write the slope-intercept form of the equation.

    Slope = 6, passing through (-5,9)
    Step 1 (point-slope)

    y - y1 = m(x - x1)

    y - 9 = 6(x - (-5))

    Step 2 (Slope-intercept form)

    y - 9 = 6x + 30

    y= 6x + 39
  51. Find the slope of the line passing through the pair of points or state that the slope is undefined. Then indicate whether the line through the points rises, falls, is horizontal or vertical.

    (-1,6) and (4,5)
    Slope is negative

    line falls from left to right
  52. Find the slope of the line passing through the pair of points or state that the slope is undefined. Then indicate whether the line through the points rises, falls, is horizontal or vertical.

    (-2,3) and (7,3)
    Slope is 0

    The line is horizontal
  53. Given the slope and y-int of the line whose equation is given. Give the steps to graph this properly.

    y = -5x+1
    The slope is -5

    The y-intercept is 1

    Step 1

    Find the y-int, then from that point rise -5 and run 1
  54. Put the following in a linear equation in slope-intercept form and state what direction the line on the graph would be.

    y=2
    y = mx + 2
  55. Put the following in a linear equation in slope-intercept form and state the slope and what the y-intercept is.

    y = 2/3x
    y= 2/3x + b

    slope is 2/3

    y-int is 0
  56. Put the following in slope-intercept form and state the slope.

    x = 5
    y= mx + b

    y = m5 + 0

    • y2 - y1 = 1 + 0 (When y is zero, use 1+0)
    • _________________________________
    • x2 - x1 = 5- 5

    1/0 = undefined
  57. Write an equation of the line

    Horizontal: through (0, -3)

    What is the equation of the line in standard form?
    ax + by = c

    x=c

    x + (-3) = 0

    x = 0/3 = 0
  58. a. Rewrite the equation 2x + y + 1 = 0 in slope-int form.
    b. Give the slope and y-int
    c. List steps to graph the slope and y-int
    • a. 2x+y+1 = 0
    •     y = -2x - 1

    • b. y = mx+b
    •     y = -2x - 1

    • c. y = -1
    •    m = -2 = -2 / 1 = RISE/RUN
  59. Determine the x and y intercepts with the equation below.
    solve x

    • 5x + 5y + 25 = 0
    • 5x + 5(0) + 25 = 0
    • 5x + 25 = 0
    • 5x = -25
    • x = -5

    • Solve for y
    • 5x + 5y + 25 = 0
    • 5(0) + 5y + 25 = 0
    • 5y + 25 = 0
    • 5y = -25
    • y=-5
  60. Find the slope of the line that is (a) parallel and (b) perpendicular to the line through the pair of points.
Author
scooby398
ID
350454
Card Set
College Algebra
Description
College Algebra
Updated