Name:_________________
Instructor:________________
Math 143 Final Exam Review
1. Solve the absolute value equation below for x.
2. Solve the following formula for the specified variable.
3. Solve the following quadratic equation by factoring.
4. Solve the equation
by extracting square roots.
5. Use the Quadratic Formula to solve
.
Date:______________
6. Solve the rational equation below.
7. Use the power principle to solve the following radical equation.
8. Find all the real solutions of the following equation by first rewriting the equation as a quadratic
equation.
9. Use interval notation to express the solution set of the inequality below.
10. Use the critical value method to solve the polynomial inequality below. Use interval notation to
write the solution set.
11. Use the critical value method to solve each rational inequality. Write each solution set in interval
notation.
12. Find an equation of a circle that satisfies the following condition. Write your answer in standard
form.
Center:
; passing through
13. Find the center and radius of the graph of the circle. The equation of the circle is written in general
form.
14. Evaluate the function at the specified value of the independent variable and simplify.
15. Evaluate the function at the specified value of the independent variable and simplify.
16. Find the domain of the function.
17. Use the vertical line test to determine if the following graph is the graph of a function.
18. Determine the intervals over which the function is increasing, decreasing, or constant.
19. Find the value of x in the domain of
20. Write the quadratic function
for which
.
in standard form.
21. Find the maximum or minimum value of the function below. State whether this value is a maximum
or a minimum.
22. The height in feet of a projectile with an initial velocity of 96 feet per second and an initial height of
50 feet is a function of time t, in seconds, given by
height of the projectile.
23. Determine whether
. Find the maximum
is an even function, an odd function, or neither.
24. Use the graph of g, shown below, to sketch the graph of the function below.
g
25. Use the graph of g, shown below, to sketch the graph of the function below.
g
26. Use the graph of E, shown below, to sketch the graph of the function below.
E
27. Use the graph of
shown below, to sketch the graph of the function below.
28. Find ( f / g )(x).
29. If
and
30. Find the difference quotient of
31. Find
.
, find
and state the domain.
.
32.
Evaluate the following composite function if
and
.
33. Describe the right-hand and the left-hand behavior of the graph of
34. Find the real zeros of the polynomial function
.
by factoring.
35. Determine the x-intercepts of the graph of the polynomial below. For each x-intercept, use the Even
Theorem to determine whether the graph of the polynomial crosses the xand Odd Powers of
axis or intersects but does not cross the x-axis.
36. Use the Rational Zero Theorem to list all possible rational zeros of the polynomial function
.
37. Use Descartes' Rule of Signs to state the number of possible positive and negative real zeros of the
polynomial function below.
38. Find all real solutions of the polynomial equation
39. Find all the zeros of the polynomial function
.
and write the polynomial as a
product of its linear factors.
40. Use the given zero to find the remaining zeros of the polynomial function below.
41. Find a polynomial function of lowest degree with integer coefficients, whose leading coefficient is
one, and that has the zeros –7,
, and 6i.
42. Determine the domain of the rational function below.
43. Which of the following is the graph of the given equation?
a.
d.
b.
e.
c.
44. Determine the vertical and horizontal asymptotes of the rational function below.
45. Determine the vertical and slant asymptotes of the rational function below.
46. Sketch the graph of the rational function
y
5
4
3
2
1
–5
–4
–3
–2
–1
–1
–2
–3
–4
–5
1
2
3
4
5
x
.
47. Draw the graph of the inverse relation.
48. Use composition of functions to determine whether
and
are inverses
of one another.
49. For
, find
. State any restrictions on the domain of
50. For
, find
. State any restrictions on the domain of
51. Explain how to use the graph of
to produce the graph of
.
.
.
52. Evaluate the logarithm below.
53. Find the domain of the function
.
54. Expand the logarithmic expression
Assume all variable expressions represent positive
real numbers.
55. Write the expression below as a single logarithm with a coefficient of 1. Assume all variable
expressions represent positive real numbers.
56. Evaluate the logarithm
using the change of base formula. Round to 3 decimal places.
57. Use algebraic procedures to find the exact solution of the equation
58. Use algebraic procedures to find the exact solution of the equation
.
.
59. An initial investment of $7000 grows at an annual interest rate of 4% compounded continuously.
How long will it take to double the investment?
60. Find the vertex and focus of the parabola.
61. Find the equation in standard form of the parabola with focus
and directrix
.
62. Find the center and vertices of the ellipse.
63. Find the center of the ellipse given by the equation
.
64. Find the equation in standard form of an ellipse with center at (0, 0) minor axis of length 30, and foci
at (0, –20) and (0, 20).
65. Find the vertices and asymptotes of the hyperbola.
66. Graph the hyperbola given by the equation
.
67. Find the standard form of the equation of the hyperbola with the given characteristics.
vertices:
foci:
68. Identify the graph of the equation below as a parabola, an ellipse, or a hyperbola.
69. Solve each system of equations by the elimination method.
70. Solve the system of linear equations.
71. Solve the system of equations below.
72. Sketch the graph of the inequality below.
y
5
4
3
2
1
–5
–4
–3
–2
–1
–1
1
2
3
4
5
x
–2
–3
–4
–5
73. Sketch the graph of the solution set of each system of inequalities.
y
5
4
3
2
1
–5
–4
–3
–2
–1
–1
–2
–3
–4
–5
1
2
3
4
5
x
74. Use the Binomial Theorem to expand and simplify the expression.
75. One acetic acid solution is 30% water and another is 80% water. How many liters of each solution
should be mixed to produce 25 liters of a solution that is 50% water?