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1. |
Which is the graph of the inequality x > -2? |
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A. |
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B. |
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C. |
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D. |
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Hint |
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2. |
If you use the elimination method to solve the system of equations
3x - 4y = 9 and 2x + 3y = 7, which of the following would be the best method?
Method I: Multiply both sides of the first equation by 2, and multiply both sides of the second equation by 3. Then add the two equations.
Method II: Multiply both sides of the first equation by 3, and multiply both sides of the second equation by 4. Then add the two equations.
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A. |
Both Method I and Method II are correct. |
B. |
Method I |
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C. |
Method II |
D. |
Neither Method I nor Method II is correct. |
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Hint |
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3. |
If you use the substitution method to solve the system of equations
3x - 2y = 4 and x + y = 5, which of the following would be the best method?
Method I: Solve the second equation for x, and substitute 5 - y for x into the first equation.
Method II: Solve the second equation for y, and substitute 5 - x for y into the first equation.
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A. |
Method I |
B. |
Neither Method I nor Method II is correct. |
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C. |
Both Method I and Method II are correct. |
D. |
Method II |
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Hint |
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4. |
Solve the system of equations by elimination.
2x + y - z = 3
x + y + z = 5
x - 2y + z = 2
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A. |
(1, 2, 1) |
B. |
(2, 1, 2) |
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C. |
(2, 2, 1) |
D. |
(1, 1, 2) |
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Hint |
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5. |
Suppose a lumber mill can turn out up to 900 units of product each week. The mill must produce at least 100 units of lumber and 400 units of plywood. Write the constraints as a system of inequalities where x = the number of units of lumber and y = the number of units of plywood. |
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A. |
x  100, y  400, and
x + y 900 |
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B. |
x 100, y 400, and
x + y 900 |
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C. |
x 100, y 400, and
x + y 900 |
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D. |
x 100, y 400, and
x + y 900 |
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Hint |
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6. |
Describe how the graphs of f(x) = |2x| and g(x) = -|2x| are related. |
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A. |
The graph of g(x) is a reflection of the graph of f(x) over the x-axis. |
B. |
The graph of g(x) is a reflection of the graph of f(x) over the x- and y-axes. |
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C. |
None are true. |
D. |
The graph of g(x) is a reflection of the graph of f(x) over the y-axis. |
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Hint |
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7. |
If you use the parent graph y =  as a reference, describe how you
would graph y =  . |
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A. |
Move the parent graph 2 units to the right and then up 5 units. |
B. |
Move the parent graph 2 units to the left and then down 5 units. |
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C. |
Move the parent graph 2 units to the right and then down 5 units. |
D. |
Move the parent graph 2 units to the left and then up 5 units. |
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Hint |
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8. |
If you use the parent graph y = x2 as a reference, describe how you would
graph y = -x2 - 3. |
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A. |
Reflect the parent graph over the y-axis and then move the graph to the left 3 units. |
B. |
Reflect the parent graph over the x-axis and then move the graph up 3 units. |
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C. |
Reflect the parent graph over the y-axis and then move the graph down 3 units. |
D. |
Reflect the parent graph over the x-axis and then move the graph down 3 units. |
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Hint |
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9. |
If y varies directly as the cube of x and y = 30 when x = 2, find x when
y = 468.75. |
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A. |
7 |
B. |
9 |
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C. |
3 |
D. |
5 |
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Hint |
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10. |
Suppose y varies directly as x and y = 13 when x = 7. Find the constant of variation and write an equation. |
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A. |
k =  and y = x |
B. |
k = and y = 13 · 7x |
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C. |
k =  and y = 13 · 7x |
D. |
k = and y = x |
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Hint |
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11. |
State the number of complex roots of the equation x4 - 3x2 - 4 = 0. |
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A. |
4 |
B. |
3 |
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C. |
1 |
D. |
2 |
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Hint |
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12. |
Solve  - x + 1 = 0. |
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A. |
-1, -2 |
B. |
1, -2 |
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C. |
1, 2 |
D. |
-1, 2 |
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Hint |
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13. |
Determine the type of polynomial function that could be used to represent the data in the following scatter plot. |
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A. |
quadratic |
B. |
linear |
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C. |
cubic |
D. |
quartic |
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Hint |
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14. |
Find the first three iterates of the function g(x) = x2 + x for an initial value of x0 = 1. |
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A. |
 = 2
 = 6
 = 42 |
B. |
= 2
= 6
= 12 |
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C. |
= 2
= 6
= 36 |
D. |
= 0
= 2
= 4 |
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Hint |
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15. |
Write an equation in slope-intercept form with a slope of  that passes through the point (-3, -5). |
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A. |
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B. |
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C. |
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D. |
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Hint |
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16. |
Sketch the graph of the function f(x) =  (x + 1)3 + 2. |
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A. |
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B. |
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C. |
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D. |
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Hint |
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17. |
Solve |3x + 5| - 4 < 2. |
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A. |
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B. |
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C. |
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D. |
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Hint |
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18. |
Given the function f(x) =  , find the inverse. |
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A. |
f -1(x) = 4  |
B. |
f -1(x) = 1 |
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C. |
f -1(x) = x - 4 |
D. |
f -1(x) =  |
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Hint |
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19. |
Determine the intervals on which the function f(x) =  is increasing and the intervals on which the function is decreasing. |
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A. |
increasing for all x |
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B. |
increasing for x < -1 and x > -1 |
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C. |
decreasing for x < -1 and increasing for x > -1 |
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D. |
increasing for x < -1 and decreasing for x > -1 |
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Hint |
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20. |
Graph the function  |
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A. |
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B. |
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C. |
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D. |
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Hint |
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