PMI Rational Expressions & Equations Unit

Variation

Class Work

  1. y varies inversely with x. If when find y when
  1. y varies inversely with x. If when find x when.
  1. y varies inversely with x2. If when,find y when.
  1. Circumference varies directly with area of a circle and inversely with the radius. Find the constant of variation if when and . What is radius whenand ?
  1. y varies jointly with x and z. If whenand ,find y when and .
  1. y varies jointly with x and z. If whenand ,find x when and .
  1. V varies jointly with and h. If whenand , find r when and

Variation

Homework

  1. y varies inversely with x. If when, find y when.
  1. y varies inversely with x. If when,find x when .
  1. y varies inversely with x2. If , when,find y when.
  1. Area of a triangle varies jointly with its height and base. Find the constant of variation if when and . What is base when and ?
  1. y varies jointly with x and z. If when and , find y when and .
  1. y varies jointly with x and z. If whenand ,find x when and .
  1. V varies jointly with and h. when and , find r when and

Reducing Rational Expressions

Class Work

Simplify.

  1. .
/ / /

Reducing Rational Expressions

Homework

Simplify.

Multiplying & Dividing Rational Expressions

Class Work

Perform the indicated operation. Write answer in simplified form.

  1. A rectangular shaped “dartboard” has dimensions (3x +3) by (2x+1) inches. On the board is a square with sides (x+1) inches. What is the probability that a randomly thrown dart that hits board lands in the square?

Multiplying & Dividing Rational Expressions

Homework

Perform the indicated operation. Write answer in simplified form.

  1. A rectangular shaped “dartboard” has dimensions (4x+6) by (2x+3) inches. On the board is a square with sides (2x+3) inches. What is the probability that a randomly thrown dart that hits board lands in the square?

Adding and Subtracting Rational Expressions

Class Work

Perform the indicated operation. Write answer in simplified form.

Adding and Subtracting Rational Expressions

Homework

Perform the indicated operation. Write answer in simplified form.

Solving Rational Equations

Class Work

Solve for x. Check for extraneous solutions.

Solving Rational Equations

Homework

Solve for x. Check for extraneous solutions.

Graphing Rational Expressions

Class Work

Graph the following functions. Clearly indicate any x-intercepts, y-intercepts, asymptotes and holes (discontinuities) on the graph, noting them in the spaces provided below.

x-intercepts: ______
y-intercepts: ______
Holes: ______
Vertical asymptotes: ______
Horizontal asymptotes: ______/ x-intercepts: ______
y-intercepts: ______
Holes: ______
Vertical asymptotes: ______
Horizontal asymptotes: ______/ x-intercepts: ______
y-intercepts: ______
Holes: ______
Vertical asymptotes: ______
Horizontal asymptotes: ______
x-intercepts: ______
y-intercepts: ______
Holes: ______
Vertical asymptotes: ______
Horizontal asymptotes: ______/ x-intercepts: ______
y-intercepts: ______
Holes: ______
Vertical asymptotes: ______
Horizontal asymptotes: ______/ x-intercepts: ______
y-intercepts: ______
Holes: ______
Vertical asymptotes: ______
Horizontal asymptotes: ______

Graphing Rational Expressions

Homework

Graph the following functions. Clearly indicate any x-intercepts, y-intercepts, asymptotes and holes (discontinuities) on the graph, noting them in the spaces provided below.

x-intercepts: ______
y-intercepts: ______
Holes: ______
Vertical asymptotes: ______
Horizontal asymptotes: ______/ x-intercepts: ______
y-intercepts: ______
Holes: ______
Vertical asymptotes: ______
Horizontal asymptotes: ______/ x-intercepts: ______
y-intercepts: ______
Holes: ______
Vertical asymptotes: ______
Horizontal asymptotes: ______
x-intercepts: ______
y-intercepts: ______
Holes: ______
Vertical asymptotes: ______
Horizontal asymptotes: ______/ x-intercepts: ______
y-intercepts: ______
Holes: ______
Vertical asymptotes: ______
Horizontal asymptotes: ______/ x-intercepts: ______
y-intercepts: ______
Holes: ______
Vertical asymptotes: ______
Horizontal asymptotes: ______

Unit Review - Multiple ChoiceName: ______

Choices are provided to support your answer, not to use as a guess & check solution to the problem. Your test will NOT be multiple choice; be prepared for that.

  1. Simplify
  1. Simplify
  2. 1
  1. Simplify
  1. Simplify
  1. Simplify
  1. The function has which of the following discontinuities?
  2. Vertical asymptotes at
  3. Removable discontinuity at
  4. Vertical asymptote at ; removable discontinuity at
  5. Vertical asymptote at ; removable discontinuity at
  1. h varies inversely with t. If when,find t when .
  2. 2
  3. 3
  4. 48
  1. The volume of a cone varies jointly to its height and the square of the radius of its base. If V= 18 when and . What is the radius when V=12 and h=4?
  2. 1
  3. 3
  4. 6
  5. 9
  1. Simplify
  1. Solve:
  2. 4
  3. 8
  4. 14
  5. no solution
  1. Solve:
  2. -1
  3. 1
  4. 6
  5. no solution
  1. Solve:
  2. -25
  3. -8
  4. 8
  5. no solution

Extended Response

  1. At math camp the lap pool is a rectangle that is by , the wading pool is a square with sides.
  2. How many times larger is the lap pool than the wading pool?
  1. If the wading pool is deep, what is the pool’s volume?
  1. If the lap pool has a depth of , how many times larger is the volume of the lap pool to the wading pool?
  1. Determine each of the following for the graph of the rational function and graph the function.

x-intercepts: ______

y-intercepts: ______

holes: ______

vertical asymptotes: ______

horizontal asymptotes: ______

PMI Rational Expressions, Equations and Functions- SOLUTIONS:

Variation:
Classwork:
1.
2.
3.
4.
5.
6.
7.
Variation:
Homework:
8.
9.
10.
11.
12.
13.
14. / Reducing Rational Expressions:
Classwork:
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36. / Reducing Rational Expressions:
Homework:
37.
38.
39.
40.
41.
42.
43.
44.
45.
46.
47.
48.
49.
50.
51.
52.
53.
54.
55.
56.
57.
58.

Math III – Rational Expressions & Equations~1~

Math III – Rational Expressions & Equations~1~

Multiplying & Dividing Rational Expressions
Class Work:
59.
60.
61.
62.
63.
64.
65.
66.
67.
68.
69.
70.
71.
72.
73.
74.
75.
76.
77. / Multiplying & Dividing Rational Expressions
Homework
78.
79.
80.
81.
82.
83.
84.
85.
86.
87.
88.
89.
90.
91.
92.
93.
94.
95.
96. / Adding & Subtracting Rational Expressions
Classwork
97.
98.
99.
100.1
101. 3
102. -1
103.
104.
105.
106.
107.
108.
109.
110.
111.
112.
113.

Math III – Rational Expressions & Equations~1~

Adding and Subtracting Rational Expressions
Homework
114.
115.
116.
117.
118.
119.
120.
121.
122.
123.
124.
125.
126.
127.
128.
129.
130. / Solving Rational Equations
Class Work
131.
132.
133.
134.
135.
136.
137.
138.
139.
140.No Solution
141.
142.
143. / Solving Rational Equations
Homework
144.
145.
146.
147.-8/15
148.
149.
150.
151.3+/-√13
152.
153.
154.
155.
156.

Graphing Rational Equations Classwork:


x-intercepts: None
y-intercepts:
Holes: None
Vertical asymptotes:
Horizontal asymptotes: /
x-intercepts: None
y-intercepts:
Holes: None
Vertical asymptotes:
Horizontal asymptotes:

x-intercepts: None
y-intercepts:
Holes:
Vertical asymptotes:
Horizontal asymptotes: /
x-intercepts: None
y-intercepts:
Holes:
Vertical asymptotes:
Horizontal asymptotes:

x-intercepts:
y-intercepts:
Holes:
Vertical asymptotes:
Horizontal asymptotes: /
x-intercepts:
y-intercepts:
Holes:
Vertical asymptotes:
Horizontal asymptotes:

Math III – Rational Expressions & Equations~1~

Graphing Rational Equations Homework:


x-intercepts: None
y-intercepts:
Holes: None
Vertical asymptotes:
Horizontal asymptotes: /
x-intercepts: None
y-intercepts:
Holes: None
Vertical asymptotes:
Horizontal asymptotes:

x-intercepts: None
y-intercepts:
Holes:
Vertical asymptotes:
Horizontal asymptotes: /
x-intercepts: None
y-intercepts:
Holes:
Vertical asymptotes:
Horizontal asymptotes:

x-intercepts:
y-intercepts:
Holes:
Vertical asymptotes:
Horizontal asymptotes: /
x-intercepts:
y-intercepts:
Holes:
Vertical asymptotes:
Horizontal asymptotes:

Unit Review - Multiple Choice

Math III – Rational Expressions & Equations~1~

  1. B.
  2. C.
  3. A.
  4. A.
  5. C.
  6. A.
  7. B.
  8. D.
  9. D.
  10. C.
  11. D.
  12. A.

Math III – Rational Expressions & Equations~1~

Extended Response

  1. a.

b.

c.

x-intercepts:

y-intercepts:

Hole:

Vertical Asymptote:

Horizontal Asymptote:

Math III – Rational Expressions & Equations~1~