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Precalculus Semester Review

Short Answer

Use the graph to determine the domain and range of the relation, and state whether the relation is a function.

1.

2.

3. Evaluate f 4 if f x 8x2 7x 7

4. Given f x x 2 7 and g x x 4

x. Find g f

1 .

[Hint: g f

4 g f 4

]

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Graph the function.

5. f(x) 5x 2 if x 2

2x 2 if x 2

6. Use the graph of y = |x| to graph y 4 x .

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7. The graph below is a portion of a complete graph. Sketch the complete graph assuming it is odd.

8. Is the following function an even function, an odd function, or neither?

Identify the change in the parent function that will produce the related function shown as a dashed line.

9. f (x) x 2

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10. f (x) x

11. f(x) x 3

12. Given:

Then state whether f 1 x is a function.

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13. Use symmetry to graph the inverse of the function.

Without graphing, describe the end behavior of the graph of the function.

14. g(x) 2x4 1

As x ___, g(x) ___

As x ___, g(x) ___

15. f (x) 4x 5x3

As x ___, g(x) ___

As x ___, g(x) ___

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Graph the function. Determine the interval(s) for which the function is increasing and the interval(s) for which the function is decreasing.

16. y x 3 0.5x2 10x 2

17. y x 2 9

x 5

18. Give the angle measure represented by 7.25 rotations counterclockwise.

19. Find the least positive angle measurement that is coterminal with 40.

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Find the values of the sine, cosine, and tangent for A.

20.

Find the values of the six trigonometric ratios for A.

21.

22. If cos 35

, find tan .

23. Find sin if is an angle in standard position and the point with coordinates (4, 3) lies on the terminal side of the angle.

24. Find the values of the six trigonometric functions of an angle in standard position if the point with coordinates (2, 4) lies on its terminal side.

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25. If c = 23 and B 69, find a. Round to the nearest tenth.

Solve the equation if 0 x 360.

26. tanx 3

27. sinx 2

2

28. If t = 21 and r = 15, find S . Round to the nearest tenth.

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29. In right triangle ABC, A = 15, c = 37, and C is the right angle. Solve the triangle. Round to the nearest tenth, if necessary.a = A =

b = B =

c = C =

30. Solve triangle ABC given that A = 56°, B = 57°, and b = 9.a = A =

b = B =

c = C =

31. Find the area of the triangle with A = 42, b = 8 feet, and c = 5 feet. Round to the nearest tenth.

32. How many triangles are there that satisfy the conditions a = 4, b = 5, 73?

33. Find all solutions for the triangle with e 25, g 29, E 36. If no solutions exist, write none. Round to the

nearest tenth.

34. Change 7

10 radians to degree measure.

35. Change 75 to radian measure in terms of .

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36. For a circle of radius 9 feet, find the arc length s subtended by a central angle of 52.

37. Find the area of a sector with a central angle of 2

15 and a radius of 18.8 m. Round to the nearest tenth.

38. A truck driver travels at 58 miles per hour. The truck tires have a diameter of 26 inches. What is the angular velocity of the wheels in revolutions per minute (rpm)?

39. A pulley of radius 15 cm turns at 8 revolutions per second. What is the linear velocity of the belt driving the pulley in meters per second?

40. Use the graph of the sine function below to find the values of for which sin 0.