Test 2 Review Math 1111 College Algebra

1. Begin by graphing the standard quadratic function f(x) = x2 . Then use transformations

of this graph to graph the given function.

g(x) = x2 + 2

*a.

b.

c.

d.

2. Begin by graphing the standard absolute value function f(x) = . Then use

transformations of this graph to graph the given function.

a.

*b.

c.

d.

3. Use the graph of the function f, plotted with a solid line, to sketch the graph of the

given function g.

g(x) = f(x) + 2

a.

b.

*c.

d.

4. Begin by graphing the standard quadratic function f(x) = x2 . Then use transformations

of this graph to graph the given function.

h(x) = (x + 2)2

a.

*b.

c.

d.

5. Use the graph of the function f, plotted with a solid line, to sketch the graph of the

given function g.

a.

*b.

c.

d.

6. Use the graph of y = f(x) to graph the given function g.

g(x) = -2f(x)

a.

*b.

c.

d.

7. Begin by graphing the standard quadratic function f(x) = x2 . Then use transformations

of this graph to graph the given function.

h(x) = (x + 7)2 - 5

a.

*b.

c.

d.

8. Begin by graphing the standard quadratic function f(x) = x2 . Then use transformations

of this graph to graph the given function.

h(x) = -(x - 2)2 + 5

*a.

b.

c.

d.

9. Begin by graphing the standard quadratic function f(x) = x2 . Then use transformations

of this graph to graph the given function.

*a.

b.

c.

d.

10. Begin by graphing the standard absolute value function f(x) = . Then use

transformations of this graph to graph the given function.

a.

*b.

c.

d.

11. Begin by graphing the standard cubic function f(x) = x3. Then use transformations of

this graph to graph the given function.

g(x) = -(x - 4)3 - 4

*a.

b.

c.

d.

12. Use the graph of the function f, plotted with a solid line, to sketch the graph of the

given function g.

g(x) = f(x + 1) - 1

*a.

b.

c.

d.

13. Find the domain of the function.

a. (- , 0) (0, )

b. (- , -13) (-13, )

*c. (- , )

d. (-13, )

14. Find the domain of the function.

f(x) =

a. (- , 19) (19, )

b. (- , ) ( , )

c. (- , ]

*d. (- , 19]

15. Find the domain of the function.

*a. (2, )

b. (- , 2) (2, )

c. [2, )

d. (- , )

16. Find the domain of the function.

f(x) =

a. (- , )

*b. (- , 4) (4, )

c. (4, )

d. (- , 0) (0, )

17. Given functions f and g, perform the indicated operations.

Find f - g.

*a. -2x - 4

b. 2x + 4

c. 8x - 8

d. -2x - 8

18. Given functions f and g, perform the indicated operations.

f(x) = 7x2 - 9x, g(x) = x2 - 7x - 18

a.

*b.

c.

d.

19. Given functions f and g, perform the indicated operations.

Find f + g.

*a. -8x + 11

b. 3x

c. 2x + 11

d. -5x + 8

20. Given functions f and g, perform the indicated operations.

Find fg.

a. (3x + 3)(3x - 5)

b. (3x + 3)(9x - 25)

c. (3x - 5)( )

*d. ( )( )

21. Given functions f and g, determine the domain of f + g.

a. (- , -4) (-4, )

b. (- , 0) (0, )

c. (0, )

*d. (- , )

22. Given functions f and g, determine the domain of f + g.

a. (- , )

b. (- , -5) (-5, )

c. (0, )

*d. (- , -2) (-2, )

23. Find the domain of the indicated combined function.

Find the domain of (f - g)(x) when f(x) = 5x - 6 and g(x) = 2x - 5.

a. Domain: (-5, 6)

b. Domain: (-6, )

c. Domain: (-6, 5)

*d. Domain: (- , )

24. For the given functions f and g , find the indicated composition.

f(x) = 15x2 - 4x, g(x) = 18x - 10

(f g)(4)

a. 13,888

b. 4022

c. 53,390

*d. 57,412

25. For the given functions f and g , find the indicated composition.

(f g)(x)

a. 15x + 35

b. 15x + 17

c. 15x + 11

*d. 15x + 7

26. For the given functions f and g , find the indicated composition.

(g f)(x)

a. 20x + 36

*b. -20x + 36

c. -20x + 30

d. -20x - 24

27. For the given functions f and g , find the indicated composition.

(f g)(x)

a.

b.

*c.

d.

28. Find the domain of the composite function f g.

a. (- , )

b. (- , -4) (-4, -3) (-3, )

*c. (- , -3) (-3, 0) (0, )

d. (- , -4) (-4, 0) (0, -3) (-3, )

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

f(x) = -3x + 8

*a.

b.

c.

d.

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

a.

b.

*c.

d.

31. Does the graph represent a function that has an inverse function?

*a. Yes

b. No

32. Does the graph represent a function that has an inverse function?

a. Yes

*b. No

33. Does the graph represent a function that has an inverse function?

a. No

*b. Yes

34. Find the distance between the pair of points.

(-5, 5) and (-11, 13)

a. 11

b. 100

*c. 10

d. 20

35. Find the distance between the pair of points.

*a. 6

b. 18

c. 5

d. 36

36. Find the midpoint of the line segment whose end points are given.

(8, -9) and (-7, 4)

a. (15, -13)

b.

*c.

d. (1, -5)

37. Find the midpoint of the line segment whose end points are given.

*a.

b.

c.

d.

38. Find the midpoint of the line segment whose end points are given.

a.

b. (17 , 19 )

*c.

d.

39. Write the standard form of the equation of the circle with the given center and radius.

(3, 9); 7

a. (x + 3)2 + (y + 9)2 = 49

*b. (x - 3)2 + (y - 9)2 = 49

c. (x - 9)2 + (y - 3)2 = 7

d. (x + 9)2 + (y + 3)2 = 7

40. Write the standard form of the equation of the circle with the given center and radius.

(0, -1); 1

a. (x - 1)2 + y2 = 1

b. x2 + (y - 1)2 = 1

*c. x2 + (y + 1)2 = 1

d. (x + 1)2 + y2 = 1

41. Write the standard form of the equation of the circle with the given center and radius.

a. (x - 1)2 + (y + 6)2 = 25

*b. (x - 6)2 + (y + 1)2 = 5

c. (x + 1)2 + (y - 6)2 = 25

d. (x + 6)2 + (y - 1)2 = 5

42. Write the standard form of the equation of the circle with the given center and radius.

(0, 0); 12

*a. x2 + y2 = 144

b. x2 + y2 = 24

c. x2 + y2 = 12

d. x2 - y2 = 12

43. Find the center and the radius of the circle.

(x - 7)2 + (y - 3)2 = 81

a. (-7, -3), r = 81

b. (-3, -7), r = 81

*c. (7, 3), r = 9

d. (3, 7), r = 9

44. Graph the equation and state its domain and range. Use interval notation

x2 + y2 = 4

a.

Domain = (- , ); Range = (- , )

*b.

Domain = (-2, 2); Range = (-2, 2)

45. Complete the square and write the equation in standard form. Then give the center

and radius of the circle.

x2 + 8x + 16 + y2 + 14y + 49 = 81

a. (x + 7)2 + (x + 4)2 = 81

(7, 4), r = 81

b. (x + 4)2 + (x + 7)2 = 81

(4, 7), r = 81

c. (x + 7)2 + (x + 4)2 = 81

(-7, -4), r = 9

*d. (x + 4)2 + (x + 7)2 = 81

(-4, -7), r = 9

46. Complete the square and write the equation in standard form. Then give the center

and radius of the circle.

x2 + y2 - 8x - 14y = -56

a. (x - 4)2 + (x - 7)2 = 9

(-4, -7), r = 9

*b. (x - 4)2 + (x - 7)2 = 9

(4, 7), r = 3

c. (x - 7)2 + (x - 4)2 = 9

(7, 4), r = 3

d. (x - 7)2 + (x - 4)2 = 9

(-7, -4), r = 9

47. Graph the equation.

x2 + y2 + 4x + 6y - 3 = 0

a.

*b.