Math 1314: College Algebra - Review Items for the Final Exam. 1. Find the
domain of the function. 2. Solve the equation by extracting square roots. 3. Use
the ...
Math 1314: College Algebra - Review Items for the Final Exam
1. Find the domain of the function.
2. Solve the equation
3. Use the Vertical Line Test to determine in which of the graphs y is not a function of x.
by extracting square roots.
a.
b.
c.
d.
e. All of the choices (A, B, C, and D) represent functions.
4. Determine the intervals over which the function is increasing, decreasing, or constant.
5. Solve the following quadratic equation.
6. Find all solutions to the following equation.
7. Evaluate ( fg )(1) for
8. Determine which point does not lie on the graph of the equation
and
.
a. (–5, –13) b. (–14, –22) c. (–12, –20) d. (–16, –24) e. (–8, –13)
.
9. Find the x-‐ and y-‐intercepts of the graph of the equation
.
10. Use algebraic tests to check the following for symmetry with respect to the axes and the origin. 11. Write the standard form of the equation of the circle with the given characteristics. center:
; radius: 4
12. Write the standard form of the equation of the circle with the given characteristics. center:
; solution point:
13. Determine the vertex of the graph of the quadratic function 14. From the graph of the quadratic function
. , determine the equation of the axis of symmetry.
15. Solve the equation and write complex solutions in standard form.
16. Describe the right-‐hand and the left-‐hand behavior of the graph of 17. Find all real zeros of the polynomial
. and determine the multiplicity of each.
18. Find the quotient and remainder when
is divided by x – 5
19. Determine the vertical and horizontal asymptotes of
20. Graph
21. Find the distance between the two points
and
.
22. Determine which ordered pair is a solution of the system.
a. (–2, 1) b. (–4, –5) c. (2, 1) d. (–5, 4) e. (1, –2) 23. Find the midpoint between the two points 24. Rewrite the exponential equation
25. Simplify the expression
26. Solve
27. Solve the system.
and
.
in logarithmic form.
.
for x.
28. Solve the system.
29. If possible, find 2A – 5B.
30. Write the slope-‐intercept form of the equation of the line through the given point perpendicular to the given line. point: (–7, –8) line: –9x – 45y = 9
31. Evaluate the function for
and simplify.
32. Find all real values of x such that f (x) = 0 given
33. Find the difference quotient and simplify your answer.
34. Use the graph of the function to find the domain and range of f. 35. Use the graph of
to write an equation for the function whose graph is shown.
36. Write an equation for the function that is described by the following characteristics: the shape of
, but moved eight units down, two units to the left, and then reflected in the x-‐axis
37. Find ( f + g)(x) given 38. Find
and
given
and
39. Find the inverse function of
.
40. Find the standard form of the quadratic function shown below:
41. A farmer has 336 feet of fencing and wants to build two identical pens for his prize-‐winning pigs. The pens will be arranged as shown. Determine the dimensions of a pen that will maximize its area.
42. The height,
, of a punted rugby ball is given by h(x) = −
1 2 13 x + x + 2 where x is the horizontal distance in 64 32
feet from the point where the ball is punted. How far, horizontally, is the ball from the kicker when it is at its highest point? 43. Find all real zeros of the polynomial 44. Divide.
45. Divide. 46. If
and determine the multiplicity of each.
, use synthetic division to evaluate
47. If is a root of real solutions of the equation.
.
, use synthetic division to factor the polynomial completely and list all
48. Using the factors and , find the remaining factor(s) of and write the polynomial in fully factored form. 49. Find all zeros of the function
.
50. Find all the rational zeros of the function 51. Given
, find any vertical asymptotes.
.
52. Determine the equations of any horizontal and vertical asymptotes of
.
53. Determine the equations of any horizontal and vertical asymptotes of 54. Solve the following equation for x.
55. Solve the following equation for x.
56. Rewrite the logarithmic equation
in exponential form.
57. Solve the equation
for x using the One-‐to-‐One Property.
58. Find the exact value of
without using a calculator.
59. Condense the expression
to the logarithm of a single term.
60. Condense the expression
to the logarithm of a single term.
61. Solve the system for “x”:
62. Solve the system for “y.”
63. Find the determinant of the matrix
.
64. Solve for x given the following equation involving a determinant.
65. Solve:
.
66. Solve. Give the solution using interval notation:
67. Solve. Give the solution using interval notation.
68. List all possible rational zeros given by the Rational Zeros Theorem. Do not check to see which actually are zeros. 69. Solve the equation. 70. Find the domain of
Math 1314: College Algebra - Review Items for the Final Exam Answer Section 1. all real numbers
2.
3. B
4.
20.
21. 26 22. A
23. 5.
6.
24.
25. –12
7. –16
26. -‐3
8. E
27. (5, 102), (–3, –34), (0, 2)
9. x-‐intercept:
y-‐intercept:
28.
10. Symmetric with respect to the y-‐axis. 11.
30.
31. 13.
(dependent)
29.
12.
14.
32.
15.
33.
range:
35.
17.
19. horizontal:
34. domain:
16. Because the degree is odd and the leading coefficient is positive, the graph falls to the left and rises to the right.
18.
36.
37. ( f + g)(x) =
38.
39.
40.
41.
42.
68.
43. 44.
45.
70.
46.
47.
;
48.
49.
50.
51. vertical asymptote
52. horizontal:
; vertical:
53. horizontal:
; vertical:
54.
55.
56.
57. –9 58. 1 59.
60.
61. 4 62. 15, 24 63. –33 64. 65. 66. 67.
69.
