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Test 1 Review Math 1111 College Algebra 1. Plot the given point in a rectangular coordinate system. (-6, -3) a. b.
Test 1 Review Math 1111 College Algebra
1. Plot the given point in a rectangular coordinate system.
(-6, -3)
a.
b.
*c.
d.
2. Plot the given point in a rectangular coordinate system.
a.
b.
c.
*d.
3. Graph the equation.
y = x + 2
a.
*b.
c.
d.
4. Graph the equation.
y = x2 - 2
a.
b.
c.
*d.
5. Graph the equation.
y = x3 + 2
*a.
b.
c.
d.
6. Graph the equation.
a.
b.
*c.
d.
7. Match the correct viewing rectangle dimensions with the figure.
a. [-10, 5, 1] by [-10, 5, 1]
b. [-5, 5, 2] by [-5, 5, 2]
*c. [-5, 5, 1] by [-5, 5, 1]
d. [-1, 1, 1] by [-1, 1, 1]
8. Use the graph to determine the x- and y-intercepts.
a. x-intercept: -6; y-intercept: 6
b. x-intercept: -3; y-intercept: -6
*c. x-intercept: -3; y-intercept: 6
d. x-intercept: 3; y-intercept: 6
9. Use the graph to determine the x- and y-intercepts.
a. x-intercept: 1
b. y-intercept: -1
c. y-intercept: 1
*d. x-intercept: -1
10. Use the graph to determine the x- and y-intercepts.
*a. x-intercepts: -3, 1, 5; y-intercept: 3
b. x-intercepts: 3, 1, -5; y-intercept: 3
c. x-intercept: 3; y-intercepts: -3, 1, 5
d. x-intercept: 3; y-intercepts: 3, 1, -5
11. Give the domain and range of the relation.
{(10, -3), (11, -4), (9, 3), (9, 9)}
a. domain = {11, 10, 9, 19}; range = {-4, -3, 3, 9}
b. domain = {11, 10, 9, -9}; range = {-4, -3, 3, 9}
c. domain = {-4, -3, 3, 9}; range = {11, 10, 9}
*d. domain = {11, 10, 9}; range = {-4, -3, 3, 9}
12. Determine whether the relation is a function.
{(2, -9), (2, 5), (4, -9), (9, 8), (10, 8)}
*a. Not a function
b. Function
13. Determine whether the relation is a function.
{(-7, 3), (-5, -6), (-1, 2), (4, -7)}
a. Not a function
*b. Function
14. Determine whether the equation defines y as a function of x.
x + y = 36
*a. y is a function of x
b. y is not a function of x
15. Determine whether the equation defines y as a function of x.
x2 + y = 9
*a. y is a function of x
b. y is not a function of x
16. Determine whether the equation defines y as a function of x.
x + y2 = 1
a. y is a function of x
*b. y is not a function of x
17. Determine whether the equation defines y as a function of x.
*a. y is a function of x
b. y is not a function of x
18. Determine whether the equation defines y as a function of x.
*a. y is a function of x
b. y is not a function of x
19. Evaluate the function at the given value of the independent variable and
simplify.
a. -14
b. -10
c. -42
*d. -26
20. Evaluate the function at the given value of the independent variable and
simplify.
a. x2 - 8x + 16
*b. x2 - 8x + 14
c. x2 - 6
d. x2 + 16
21. Evaluate the function at the given value of the independent variable and
simplify.
*a. 5x2 - 7x - 4
b. -7x2 + 5x - 4
c. 5x2 - 27x + 2
d. 5x2 - 7x + 2
22. Evaluate the function at the given value of the independent variable and
simplify.
a. 21
*b. 15
c. -15
d. -21
23. Evaluate the function at the given value of the independent variable and
simplify.
a. -4
b. 2
*c. 4
d. not a real number
24. Solve the problem.
The function P(x) = 0.85x - 80 models the relationship between the number of pretzels x
that a certain vendor sells and the profit the vendor makes. Find the profit the
vendor makes from selling 800 pretzels.
a. $760
b. $680
c. $720
*d. $600
25. Graph the given functions on the same rectangular coordinate system. Describe
how the graph of g is related to the graph of f.
f(x) = -2x, g(x) = -2x - 3
a.
g shifts the graph of f vertically up 3 units
b.
g shifts the graph of f vertically down 3 units
*c.
g shifts the graph of f vertically down 3 units
d.
g shifts the graph of f vertically up 3 units
26. Use the vertical line test to determine whether or not the graph is a graph in
which y is a function of x.
a. function
*b. not a function
27. Use the vertical line test to determine whether or not the graph is a graph in
which y is a function of x.
*a. function
b. not a function
28. Use the vertical line test to determine whether or not the graph is a graph in
which y is a function of x.
a. function
*b. not a function
29. Use the vertical line test to determine whether or not the graph is a graph in
which y is a function of x.
a. not a function
*b. function
30. Use the vertical line test to determine whether or not the graph is a graph in
which y is a function of x.
a. function
*b. not a function
31. Use the vertical line test to determine whether or not the graph is a graph in
which y is a function of x.
*a. not a function
b. function
32. Use the graph to find the indicated function value.
y = f(x). Find f(3).
*a. 1.5
b. 9
c. 3
d. -3
33. Use the graph to find the indicated function value.
y = f(x). Find f(-5)
a. -5
b. 2
c. 17
*d. 5
34. Use the graph to find the indicated function value.
y = f(x). Find f(2)
a. -5
b. 3
*c. 5
d. 0.5
35. Use the graph to determine the function's domain and range.
*a. domain: (- , )
range: (- , )
b.
c.
d. domain: (- , )
range: y = -1
36. Use the graph to determine the function's domain and range.
a. domain: [4, )
range: [-5, )
b. domain: (- , )
range: (- , )
*c. domain: (- , )
range: [-5, )
d. domain: (- , 4) or (4, )
range: (- , -5) or (-5, )
37. Use the graph to determine the function's domain and range.
a. domain: [0, )
range: [0, )
b. domain: (- , )
range: [2, )
c. domain: [0, )
range: (- , )
*d. domain: [0, )
range: [2, )
38. Identify the intercepts.
a. (-2, 0), (0, -8)
b. (-2, -2), (8, 8)
c. (2, 0), (0, 8)
*d. (-2, 0), (0, 8)
39. Identify the intercepts.
a. (1, 0), (-1, 0)
b. (1, 0), (-1, 0), (0, 0)
*c. (1, 0), (-1, 0), (0, -1)
d. (0, -1)
40.
f(x) = 3x - 8
a. 0
b.
c.
*d. 3
41.
f(x) = x2 + 2x + 6
*a. 2x + h + 2
b. 1
c. 2x + h + 6
d.
42. Evaluate the piecewise function at the given value of the independent variable.
Determine f(-5).
a. -14
b. 7
c. -15
*d. -18
43. Solve the problem.
Suppose a car rental company charges $102 for the first day and $52 for each additional
or partial day. Let S(x) represent the cost of renting a car for x days. Find the value of
S(4.5).
a. $336
b. $234
c. $284
*d. $310
44. Solve the problem.
Suppose a life insurance policy costs $32 for the first unit of coverage and then $8 for
each additional unit of coverage. Let C(x) be the cost for insurance of x units of coverage.
What will 10 units of coverage cost?
*a. $104
b. $48
c. $80
d. $112
45. Identify the intervals where the function is changing as requested.
Increasing
a. (-3, )
b. (-3, 3)
c. (-2, )
*d. (-2, 2)
46. Identify the intervals where the function is changing as requested.
Constant
a. (3, )
*b. (- , -1) or (3, )
c. (-1, 0)
d. (- , 0)
47. Identify the intervals where the function is changing as requested.
Increasing
a. (-2, )
*b. (3, )
c. (-2, 0)
d. (3, 6)
48. Identify the intervals where the function is changing as requested.
Decreasing
a. (- , -2)
b. (0, -2)
*c. (-3, -2)
d. (- , -3)
49. Identify the intervals where the function is changing as requested.
Decreasing
a. (5, 1)
b. (6, 12)
*c. (5, 12)
d. (6, 1)
50. Identify the intervals where the function is changing as requested.
Constant
a. (2, )
b. (1, 2)
*c. (-1, 1)
d. (-2, -1)
51. Use the graph of the given function to find any relative maxima and relative
minima.
f(x) = x3 - 3x2 + 1
*a. maximum: (0, 1); minimum: (2, -3)
b. no maximum or minimum
c. maximum: (0, 1); minimum: none
d. maximum: none; minimum: (2, -3)
52. Use the graph of the given function to find any relative maxima and relative
minima.
f(x) = x3 - 12x + 2
a. no maximum or minimum
b. maximum: (-2, 18) and (0, 0); minimum: (2, -14)
c. maximum: (2, -14); minimum: (-2, 18)
*d. minimum: (2, -14); maximum: (-2, 18)
53. Determine whether the given function is even, odd, or neither.
f(x) = x3 - 2x
a. Neither
b. Even
*c. Odd
54. Determine whether the given function is even, odd, or neither.
f(x) = 2x2 + x4
a. Odd
b. Neither
*c. Even
55. Determine whether the given function is even, odd, or neither.
f(x) = x3 - x2
*a. Neither
b. Odd
c. Even
56. Use possible symmetry to determine whether the graph is the graph of an even
function, an odd function, or a function that is neither even nor odd.
a. Neither
b. Odd
*c. Even
57. Use possible symmetry to determine whether the graph is the graph of an even
function, an odd function, or a function that is neither even nor odd.
a. Odd
*b. Neither
c. Even
58. Use possible symmetry to determine whether the graph is the graph of an even
function, an odd function, or a function that is neither even nor odd.
a. Even
*b. Odd
c. Neither
59. Find the slope of the line that goes through the given points.
(-4, -9), (7, -6)
a.
b.
c. - 5
*d.
60. Find the slope of the line that goes through the given points.
a.
b.
c.
*d. Undefined
61. Use the given conditions to write an equation for the line in point-slope form.
Slope = -2, passing through (5, 6)
a. y + 6 = -2(x + 5)
b. x - 6 = -2(y - 5)
c. y = -2x + 16
*d. y - 6 = -2(x - 5)
62. Use the given conditions to write an equation for the line in point-slope form.
Passing through (6, 8) and (5, 3)
a. y - 8 = 6(x + 6) or y - 3 = 5(x - 8)
b. y - 8 = 5(x - 5) or y - 3 = 5(x - 6)
*c. y - 8 = 5(x - 6) or y - 3 = 5(x - 5)
d. y + 8 = 5(x + 6) or y + 3 = 5(x + 5)
63. Use the given conditions to write an equation for the line in point-slope form.
Passing through (1, -7) with x-intercept = -1
a. y + 1 = 7x or y - 7 = 7(x - 1)
b.
*c.
d.
64. Use the given conditions to write an equation for the line in slope-intercept form.
Slope = 4, passing through (4, 6)
a. y - 6 = 4x - 4
*b. y = 4x - 10
c. y - 6 = x - 4
d. y = 4x + 10
65. Use the given conditions to write an equation for the line in slope-intercept form.
a.
b.
*c.
d.
66. Graph the line whose equation is given.
*a.
b.
c.
d.
67. Graph the equation in the rectangular coordinate system.
f(x) = 5
a.
b.
c.
*d.
68. Graph the equation in the rectangular coordinate system.
-2x + 9 = 15
a.
b.
*c.
d.
69. Determine the slope and the y-intercept of the graph of the equation.
y + 12 = 0
a. m = 1; (0, -12)
b. m = 0; no y-intercept
*c. m = 0; (0, -12)
d. m = -12; (0, 0)
70. Determine the slope and the y-intercept of the graph of the equation.
x + 10y -1 = 0
a. m = 1; (0, 1)
b.
c. m = -10; (0, 10)
*d.
71. Graph the equation.
3x + 4y - 14 = 0
a.
*b.
c.
d.
72. Graph the linear function by plotting the x- and y-intercepts.
-3x - 6y - 6 = 0
a. intercepts: (0, 2), (1, 0)
*b. intercepts: (0, -1), (-2, 0)
c. intercepts: (0, -2), (-1, 0)
d. intercepts: (0, -1), (2, 0)
73. Use the given conditions to write an equation for the line in the indicated form.
Passing through (2, 1) and parallel to the line whose equation is ;
point-slope form
a. y - 1 = x - 2
b. y - 2 = 2(x - 1)
c. y = 2x
*d. y - 1 = 2(x - 2)
74. Use the given conditions to write an equation for the line in the indicated form.
Passing through (2, 3) and perpendicular to the line whose equation is y = 4x + 7;
point-slope form
*a.
b.
c. y = - 4x - 14
d.
75. Use the given conditions to write an equation for the line in the indicated form.
Passing through (4, 3) and perpendicular to the line whose equation is
slope-intercept form
a.
b. y = - 5x - 23
c. y = 5x - 23
*d. y = - 5x + 23
76. Use the given conditions to write an equation for the line in the indicated form.
Passing through (2, 3) and perpendicular to the line whose equation is ;
slope-intercept form
*a.
b. y = - 2x - 8
c.
d.
77. Find the average rate of change of the function from x1 to x2.
a.
*b.
c. 7
d. 2
78. Find the average rate of change of the function from x1 to x2.
f(x) = -3x2 - x from x1 = 5 to x2 = 6
a.
b.
*c. -34
d. -2
79. Find the average rate of change of the function from x1 to x2.
f(x) = 5x + 7 from x1 = -1 to x2 = 0
*a. 5
b.
c.
d. -28
