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Assignment 2 MAT121 Summer 2015
NAME:_______________________
Directions: Do ALL of your work on THIS handout in the space provided! On problems that your teacher would show work on
be sure that you also show work on! This assignment is DUE on or before 8:00 a.m. Wednesday June 3td (see your syllabus for
late penalty!).
3.1 Point-Slope Formula and Review of Graphing
Find the x- and y-intercepts (when possible) and graph use them to graph each line. Be sure to list BOTH coordinates (x,y) of any
intercepts. Make appropriate markings and/or label appropriate numbers on the axes. If there is no intercept then write “none”.
1. 2x + 3y = 12
2. x – 3y = 6
3. 2x = -14
4. y + 3 = 0
x-int = ___________
y-int = ___________
x-int = ___________
y-int = ___________
x-int = ___________
y-int = ___________
x-int = ___________
y-int = ___________
Write the slope-intercept form (y= mx+b) of the line, then identify the slope and y-intercept (0,y).
1
2
x y 4
3
5
5. 3x = 5 – 2y
6. 2x + 4y = 16
7.
Slope = ___________
y-int = ___________
Slope = ___________
y-int = ___________
Slope = ___________
y-int = ___________
Find the slope of the line that passes through the given points.
8. (-2, -4) and (5, -3)
9. (5,1) and (5,4)
10. (4, -1) and (2, -1)
Use the point-slope formula (if possible) to write an equation of the line given the following information. Write the final answer in
slope-intercept form if possible.
11. The slope is
2
and the line passes through (-2,5)
3
12. The line passes through the points (5,1) and (2, 9)
3.2 Introduction to relations.
13. Write the relation as a set of ordered pairs then list the domain and range of the relation.
Group (x)
Group (y)
1
1
1
2
5
4
9
2
8
1
Find the domain and range of the relations. Write your answer in interval notation, when appropriate.
14
y
6
5
4
(3,4)
3
2
1
-6
-5
-4
-3
-2
-1
(1,2)
1
x
2
3
4
5
6
-1
-2
(-3,-2)
-3
(1,-3)
-4
-5
-6
.
Domain = ____________________ Range = ____________________
15.
14
y
12
10
(0,10)
8
6
4
2
-8
-6
-4
-2
(5,5)
(3,1)
2
-2
4
6
x
8
-4
-6
-8
-10
-12
.
-14
Domain = __________________
Range = _________________
16.
17.
Domain = ________________ Range = __________________
Domain = _________________ Range = _______________
3.3 Introduction to functions….
Which of the relations define y as a function of x? (write “function” or “not a function” next to each problem)
18.
{ (1,2) (3,4) (5,6) (7,8) (9,10)}
19. { (3,1) (4,5) (3,6) }
20.
21.
y
y
6
6
5
5
4
4
3
3
2
2
1
1
x
x
-6
-6
-5
-4
-3
-2
-1
1
2
3
4
5
-5
-4
-3
-2
-1
1
2
3
4
5
6
6
-1
-1
-2
-2
-3
-3
-4
-4
-5
-5
-6
-6
22.
23.
y
y
6
6
5
5
4
4
3
3
2
2
1
1
x
x
-6
-5
-4
-3
-2
-1
1
2
3
4
5
-6
-5
-4
-3
-2
-1
1
6
2
3
4
5
6
-1
-1
-2
-2
-3
-3
-4
-4
-5
-5
-6
-6
24.
25.
y
y
6
6
5
5
4
4
3
3
2
2
1
1
x
x
-6
-5
-4
-3
-2
-1
1
2
3
4
5
6
-6
-5
-4
-3
-2
-1
1
-1
-1
-2
-2
-3
-3
-4
-4
-5
-5
-6
-6
2
3
4
5
6
Consider the functions defined by and find the requested function values. Work should be shown on all but one of these!
f(x) = 3x + 4
g(x) x2 + 5x + 6
h(x) = 4
26. g ( - 2 )
27. f ( 3)
28. h ( 0 )
29. k ( -7 )
30. g ( a + 1 )
Refer to functions y = f(x) and y = g(x) defined as follows:
f = { (1,2) (2,3) (3,5) (9,3)}
g = { (1,-2) (5,6) (-1,17) (4,-2) (6,4)}
31. Identify the domain of f.
32. Identify the range of g
33. For what value(s) of x is f(x) = 3?
34. For what value(s) of x is g(x) = -2
35. Find f(3)
36. Find g(6)
Find the domain and write your answer in interval notation.
37.
m  x 
x2
x 3
38. g(x) = x2 – 9
3.4 Graphs of BASIC functions.
In class we discussed SIX (6) BASIC graphs that all Algebra students should know. Make a decent sketch of each on the axes below
AND label them with their correct equation!!!!! Make appropriate markings on the axes!
39.
40.
41.
42.
43.
44.
For each of the following graphs list the X and Y intercepts
 x, y 
if a graph has no intercept then write “none”.
45.
47.
46.
X-int(s) ______________
X-int(s) ______________
Y-int(s)_______________
Y-int(s) ______________
X-int(s) ______________
48.
Y-int(s) ______________
49.
X-int(s) ______________
Y-int(s) ______________
50.
X-int(s) _____________
X-int(s) _________
Y-int(s) ______________
Y-int(s) __________
Find the x- and y-intercepts for each of the following functions.
51. f(x) = 2x – 6
52. A(x) = (x+1)(3x – 2)
53. f(x) = x3 + 4x2 – 5x
3.5 Variation.
Write a variation model. Use k as the constant of variation.
54. M varies jointly as the square of x and the cube of y.
55. A varies directly as the square of B and inversely as the cube root of C
Find the constant of variation, k.
56. T varies inversely as Q and when Q is 5, T is 10.
Solve.
57. Y varies jointly as x and the square of z. Y is 48 when z is 2 and x is 3. Find Y when x is 3 and z is 4.
58. The distance a ball rolls down an inclined plane is directly proportional to the square of the time it rolls. During the first second,
the ball rolls 8 feet. How far will the ball roll during the first 3 seconds?
4.1 A Review of the Properties of Exponents
Simplify the expression.
59.
5 p q  3 pq 
3 2 2
 2x y 
 4 xy 
2
2
60.
3 3
3 2
4.2 A Review of the Properties of exponents (the power of 0 and negative exponents)
Simplify the expression. Write the answer with positive exponents only. Some work should be shown on 61, 62 and 65
 2x2 
61. 

 3y 
2
62.
63. 30
65.
 2x3 y 3 z 
64.
3
3x4 yz 2 
2
3x 2 y 6
21x5 y 4
 3
0
 2 x 2 y 3 z 
66.  5 7 4 
 4x y z 
0
4.3 Definition of nth Root
Evaluate the roots without a calculator. Identify those that are not real numbers. NO decimal answers should be given!
67.
71.
64
5
32
68.
72.
3
64
 4 16
69.
64
70.
73.
3
64
3
74.
1
8
Use a calculator to evaluate the expression, round to three decimal places.
75.
4
10
76.
6 5 35
77.
78.
6
24
Simplify without a calculator. Make no assumptions regarding variables.
79.
80.
3
82.
43
83.
3
 4 
81.
3
84.
3
x3
Simplify the radical expressions. Use absolute values when necessary.
85.
3
8x9 y12
z15
86.

9
16x 2
Simplify the expressions. Assume all variables are positive real numbers, so no absolute values will be needed in any of the
answers.
87.
3
8x9 y12
z15
88.

9
16x 2
4.4 Rational Exponents.
Write the expression using positive exponents and radical notation, then simplify. Work should be shown on all of these!
1
89.
100

3
2
90.
91.
Simplify the expression using the properties of rational exponents. Write the final answer using positive exponents.
Work should be shown on all of these!
92.
93.
94.
a

2
3
1
a2
Use a calculator to approximate the expressions and round to 4 decimal places.
4
95.
96.
6
1
2
4.5 Properties of Radicals
For this point forward , assume that all variables represent positive real numbers unless stated otherwise.
Use the multiplication property of radicals (and rules of exponents) to multiply the expressions. Then simplify the result.
97.
3
ab5  3 a8b
98.
Use the division property of radicals (and rules of exponents) to divide the expression. Then simplify the result.
99.
3
24 x
3
3x 4
 2 x  1
9
 2 x  1
5
100.
Simplify the radicals. No decimal answers!
101.
104.
3
48x6 y 2 z
102.
103.
3
105.
106.
3
4.6 Addition and Subtraction of Radicals.
Add or subtract the radical expressions if possible.
107.
108.
109.
110.
111.
3 3 250  6 3 54
2 x x  x3  5 x3
4.7 Multiplication of Radicals.
Multiply the radical expressions and simplify if possible.
112.
4
12b3  4 20b5
113.
114.
24
81xy 5
8
115.
116.
117.
4.8 Rationalization.
Rationalize the denominator.
118.
4
6
119.
4
120.
2x 5
Rationalize the denominators by multiplying by the conjugate.
121.
5
3 2
122.
2 3
5 3
2
3
5