Test 2 Review Math 1111 College Algebra 1. Begin by graphing the standard quadratic function f(x) = x 2. Then use transformations of this graph to graph the given function. g(x) = x 2 + 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) = x 2. 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) = x 2. 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) = x 2. 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) = x 2. 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) = x 3. 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) = 7x 2-9x, g(x) = x 2-7x - 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) = 15x 2-4x, 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 + y 2 = 1 b. x 2 + (y - 1) 2 = 1 *c. x 2 + (y + 1) 2 = 1 d. (x + 1) 2 + y 2 = 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. x 2 + y 2 = 144 b. x 2 + y 2 = 24 c. x 2 + y 2 = 12 d. x 2 - y 2 = 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 x 2 + y 2 = 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. x 2 + 8x + 16 + y 2 + 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. x 2 + y 2-8x - 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. x 2 + y 2 + 4x + 6y - 3 = 0
a. *b.