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Algebra Problems

1. Solve the problem.

The amount of gas that a helicopter uses is directly proportional to the number of hours spent flying. The helicopter flies for 2 hours and uses 28 gallons of fuel. Find the number of gallons of fuel that the helicopter uses to fly for 3 hours.
A) 42 gallons
B) 6 gallons
C) 45 gallons
D) 56 gallons

2. Find the slope of the line that goes through the given points.

(5, -4), (8, -2)
A)
B)
C)
D)

3. Graph the rational function.

f(x) =

A)

B)

C)

D)

4. Use the graph to determine the x- and y-intercepts.

A) x-intercept: 5
B) x-intercept: -5
C) y-intercept: -5
D) y-intercept: 5

5. Find the y-intercept for the graph of the quadratic function.

f(x) = (x + 1)2 - 1
A) (0, 0)
B) (0, 2)
C) (0, 1)
D) (0, -1)

6. Write the equation in its equivalent logarithmic form.

123 = y
A) log12 y = 3
B) log3 y = 12
C) logy 12 = 3
D) logy 3 = 12

7. Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator.

log6(7 &#8729; 11)
A) log67 + log611
B) log67 - log611
C) log677
D) (log67)(log611)

8. Find the range of the quadratic function.

f(x) = x2 + 7
A) [7, &#8734;)
B) (-&#8734;, 7]
C) [-7, &#8734;)
D) [0, &#8734;)

9. Solve the equation by expressing each side as a power of the same base and then equating exponents.

4(1 + 2x) = 64
A) {1}
B) {16}
C) {4}
D) {-1}

10. Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic expressions. Give the exact answer.

log2(6x - 3) = log2(2x + 2)
A)
B)
C) {-1}
D)

11. If y varies inversely as x, find the inverse variation equation for the situation.

y = 6 when x = 3
A) y =
B) y = 2x
C) y =
D) y =

12. Evaluate or simplify the expression without using a calculator.

log 108
A) 8
B) 10
C) log 8
D) 108

13. Write the equation in its equivalent exponential form.

log2 x = 3
A) 23 = x
B) 32 = x
C) 2x = 3
D) x3 = 2

14. Find the coordinates of the vertex for the parabola defined by the given quadratic function.

f(x) = -7(x - 2)2 - 6
A) (2, -6)
B) (-6, 2)
C) (-2, -6)
D) (-7, -2)

15. Find the average rate of change of the function from x1 to x2.

f(x) = -3x2 - x from x1 = 5 to x2 = 6
A) -34
B) -2
C)
D) -

16. Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic expressions. Give the exact answer.

log (x + 23) - log 2 = log (3x + 1)
A)
B)
C)
D)

17. Solve the problem.

Is there origin symmetry for the rational function f(x) = ?
A) Yes
B) No

18. Solve the linear inequality. Other than , use interval notation to express the solution set and graph the solution set on a number line.

- &#8804; + 2

A)

B)

C)

D)

19. Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator.

logw
A) logw7 +logwx - logw2
B) logw5x
C) logw7x -logw2
D) logw7 +logwx + logw2

20. 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 = x + 7;
slope-intercept form
A) y = - 7x + 17
B) y = 7x - 17
C) y = - 7x - 17
D) y = - x -

21. Find the inverse of the one-to-one function.

f(x) =
A) f-1(x) = x3 + 8
B) f-1(x) =
C) f-1(x) = x + 8
D) f-1(x) = x3 + 64

22. Solve the equation using the quadratic formula.

x2 + 7x + 3 = 0
A)
B)
C)
D)

23. Use the graph to determine the x- and y-intercepts.

A) x-intercept: 2; y-intercept: 8
B) x-intercept: 2; y-intercept: -8
C) x-intercept: -2; y-intercept: 8
D) x-intercept: -2; y-intercept: -8

24. Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic expressions. Give the exact answer.

log7 (x + 2) - log7 x = 2
A) { }
B) {7}
C) { }
D) {24}

25. Give the domain and range of the relation.

{(6, -7), (6, 3), (-4, -1), (-7, -6), (-3, -9)}
A) domain = {6, 12, -4, -3, -7}; range = {3, -1, -9, -6, -7}
B) domain = {3, -1, -9, -6, -7}; range = {6, 6, -4, -3, -7}
C) domain = {6, -4, -3, -7}; range = {3, -1, -9, -6, -7}
D) domain = {6, -2, -4, -3, -7}; range = {3, -1, -9, -6, -7}

Solution Summary

Solutions to all the problems are provided.

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