Download Assignment 2 MAT121 Summer 2012 NAME: Directions: Do ALL of

Assignment 2 MAT121 Summer 2012
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 May 30th (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.
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.
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 each 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.
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!!!!!
39.
40.
41.
42.
43.
44.
For each of the following graphs list the X and Y intercepts 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.
 2 x2 
61. 

 3y 
2
62.
63. 30
65.
64.
 2x y z  3x
3
3
3
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.
67.
71.
64
5
32
68.
72.
3
64
 4 16
69.
64
70.
73.
3
74.
64
3
1
8
Use a calculator to evaluate the expression, round to three decimal places.
75.
4
10
Simplify
79.
3
82.
76.
6 5 35
77.
78.
6
24
80.
43
83.
81.
3
 4
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.
1
89.
100

3
2
90.
91.
Simplify the expression using the properties of rational exponents. Write the final answer using positive exponents.
92.
93.
94.
a

2
3
1
a2
Use a calculator to approximate the expressions and round to 4 decimal places.
4
95.
96.
1
62
4.5 Properties of Radicals
For this point forward , assume that all variables represent positive real numbers unless stated.
Use the multiplication property of radicals to multiply the expressions. Then simplify the result.
97.
3
ab5  3 a8b
98.
Use the division property of radicals 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.
101.
104.
102.
3
6
2
48x y z
105.
103.
3
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