Name _________________________________________________________ Date _________
Chapter 7: Rational Functions
Students will be able to graph, simplify, add, subtract, multiply, and divide rational
functions, along with solving rational equations and work with variation.
Learning Goal
1.
2.
3.
4.
5.
6.
7.
Learning Activities: Check off if you get all of the questions right. If missed, you need more practice with that skill.
Classify direct and inverse variation #1-6
8. Divide Rational Expressions #20-21
Write inverse variation equations #7-8
9. Add/Subtract w/ common denominators #22-23
Solve inverse variation equations #7-9
10. Add/Subtract w/o common denominators #24-27
Graph simple rational functions #10-12
11. Simplify complex fractions #29
Translating simple rational functions #10-11 12. Solve rational functions by cross multiplying #30-31, 35
Simplify Rational Expressions #13-15
13. Solve rational functions by using LCD #32-34
Multiply Rational Expressions #16-18
14. Use inverse functions #36
7.1
In Exercises 1–6, tell whether x and y show direct variation, inverse variation, or neither.
1. xy  7
2. 6x  y
3. x  y  8
In Exercises 7–10, tell whether x and y show direct variation, inverse variation,
or neither.
4.
x
2
4
8
10
y
38
19
9.5
7.6
5.
x
3
5
8
10
y
15
9
6
5.5
6.
x
1.5
4
6.5
10
y
9
24
39
60
In Exercises 11–13, the variables x and y vary inversely. Use the given values to write an
equation relating x and y. Then find y when x  3.
7. x  6, y  5
8. x  3, y  2
3
9. The number y of songs that can be stored on an MP3 player varies inversely with the average size x of a song.
A certain MP3 player can store 3000 songs when the average size of a song is 5 megabytes. Find the number
of songs that will fit on the MP3 player when the average size of a song is 4 megabytes.
Copyright © Big Ideas Learning, LLC
All rights reserved.
Algebra 2
Resources by Chapter
227
7.2
In Exercises 4 –15, graph the function. State the domain, range, vertical and horizontal asymptote.
10. g  x 
3
x4
11. y 
2
3
x 1
12. g  x 
x3
2x  8
7.3
In Exercises 1–6, simplify the expression, if possible.
13.
4 x3
3x3  7 x
14.
x2  5x  6
x2  2 x  3
x 4  16
5 x3  3x 2  20 x  12
15.
In Exercises 7–12, find the product.
16.
18.
x 4  x  4
x3

x
 3 x  2
x5
x2  x  6
3x 2  12 x

x 2  8 x  16 x 2  2 x  3
17.
x2  2 x x2  6x  5

x5
3x
19.
x 2  3x  28
  x 2  8 x  15
2
x  25
21.
x2  2 x  3 x2  4 x  3
 2
x2  2 x  8
x  6x  8
In Exercises 13–16, find the quotient.
20.
x 2  10 x  21
  x 2  14 x  49
x2
228 Algebra 2
Resources by Chapter
Copyright © Big Ideas Learning, LLC
All rights reserved.
7.4
In Exercises 1–3, find the sum or difference.
22.
2 x2
8x

x6
x6
23.
3x
12

x4 x4
In Exercises 4 –7, find the least common multiple of the expressions.
24. x2  100, x  10
In Exercises 9–12, find the sum or difference.
7
4x

26.
x5
x 1
x2 3
6x
 
28.
x3
x 2x  1
Copyright © Big Ideas Learning, LLC
All rights reserved.
25. 25x2  4, 3x2  10 x  8
27.
x2  3
x5

2
x  6 x  16
x2
4
2
 2
3x
x
29.
x
4

x 1 x 1
Algebra 2
Resources by Chapter
229
7.5
In Exercises 1–3, solve the equation. Check your solution(s).
30.
3
1

4x
x2
33.
4
1
x 1


x5 x
x5
31.
3
x5

x 1
x5
34.
32.
4 2

 4
3
x
8
x8
3 
x
x4
35. For Valentine’s Day, a chocolate store plans to produce a chocolate-covered strawberry in the shape of a heart.
The initial cost for the store to produce this item is $560. The store estimates that it will cost $0.84 to make one
heart-shaped chocolate-covered strawberry. How many of the heart-shaped chocolate-covered strawberries must
the company produce before the average cost for the item is $1.25? Round your answer to the nearest whole
number.
36. Find the inverse & determine if it is a function: 𝑦 =
230 Algebra 2
Resources by Chapter
3
𝑥−5
Copyright © Big Ideas Learning, LLC
All rights reserved.