Deck 6: Rational Expressions, Equations, and Functions

Question 1

Simplify the rational expression.

A)
B)
C)
D)
E)

Answer 1

Question 2

The average cost for a manufacturer to produce x units of a product is given by . Describe the domain.

A)all
B)all
C)all
D)all integers
E)all

Answer 2

all integers

Question 3

Find the domain of the rational function.

A)
B)
C)
D)
E)

Answer 3

Question 4

Simplify the rational expression.

A)
B)
C)
D)
E)

Question 5

Simplify the rational expression.

A)
B)
C)
D)
E)

Question 6

Find the domain of the rational function.

A)
B)
C)
D)
E)

Question 7

Simplify the rational expression.

A)
B)
C)
D)
E)

Question 8

Simplify the rational expression.

A)
B)
C)
D)
E)

Question 9

Find the domain of the rational function.

A)
B)
C)
D)
E)

Question 10

Simplify the rational expression.

A)
B)
C)
D)
E)

Question 11

Find the domain of the rational function.

A)
B)
C)
D)
E)

Question 12

Find the domain of the rational function.

A)
B)
C)
D)
E)

Question 13

Find the domain of the rational function.

A)
B)
C)
D)
E)

Question 14

Simplify the rational expression.

A)
B)
C)
D)
E)

Question 15

Find the ratio of the area of the shaded portion to the total area of the figure. A = 5 and B = 6.

A)
B)
C)
D)
E)

Question 16

A machine shop has a setup cost of $3000 for the production of a new product. The cost, C, of labor and material for producing each unit is $10.75. The average cost function for producing x units is given by . Determine the domain of the average cost function.

A)all real numbers
B)all
C)all
D)all integers
E)all integers

Question 17

Evaluate the rational function at and simplify. If this is not possible, state the reason.

A)0
B)-13
C)4
D)-104
E)undefined

Question 18

Simplify the rational expression.

A)
B)
C)
D)
E)

Question 19

Simplify the rational expression.

A)
B)
C)
D)
E)

Question 20

Evaluate the rational function at and simplify. If this is not possible, state the reason.

A)85
B)55
C)6
D)42
E)undefined

Question 21

Divide and simplify.

A)
B)
C)
D)
E)

Question 22

One swimming pool is circular and another is rectangular. The rectangular pool's width is six times its depth. Its length is 12 feet more than its width. The circular pool has a diameter that is twice the width of the rectangular pool, and it is 2 feet deeper. Find the ratio of the circular pool's volume to the rectangular pool's volume.

A)
B)
C)
D)
E)

Question 23

Divide and simplify.

A)
B)
C)
D)
E)

Question 24

Multiply and simplify.

A)
B)
C)
D)
E)

Question 25

Multiply and simplify.

A)
B)
C)
D)
E)

Question 26

Fill in the missing factor.

A)
B)
C)
D)
E)

Question 27

Multiply and simplify.

A)
B)
C)
D)
E)

Question 28

Combine and simplify.

A)
B)
C)
D)
E)

Question 29

Multiply and simplify.

A)
B)
C)
D)
E)

Question 30

Divide and simplify.

A)
B)
C)
D)
E)

Question 31

Perform the operations and simplify.

A)
B)
C)
D)
E)

Question 32

Multiply and simplify.

A)
B)
C)
D)
E)

Question 33

Multiply and simplify.

A)
B)
C)
D)
E)

Question 34

A machine shop has a setup cost of $3900 for the production of a new product. The cost, C, of labor and material for producing each unit is $7.25. The average cost function for producing x units is given by . Find .

A)$37.25 per unit
B)$51.625 per unit
C)$23.625 per unit
D)$55.625 per unit
E)$22.625 per unit

Question 35

Multiply and simplify.

A)
B)
C)
D)
E)

Question 36

Multiply and simplify.

A)
B)
C)
D)
E)

Question 37

Perform the operations and simplify.

A)
B)
C)
D)
E)

Question 38

Divide and simplify.

A)
B)
C)
D)
E)

Question 39

Multiply and simplify.

A)
B)
C)
D)
E)

Question 40

Multiply and simplify.

A)
B)
C)
D)
E)

Question 41

Combine and simplify.

A)
B)
C)
D)
E)

Question 42

The number of males M (in thousands)and the number of females F (in thousands)participating in high school athletic programs from 1995 through 2001 can be modeled by and . In these models, t represents the year, with corresponding to 1995. Find a rational model that represents the total number T of participants in high school athletic programs.

A)
B)
C)
D)
E)

Question 43

Find the least common denominator of the two fractions and rewrite each fraction using the least common denominator.

A)
B)
C)
D)
E)

Question 44

Combine and simplify.

A)
B)
C)
D)
E)

Question 45

Combine and simplify.

A)
B)
C)
D)
E)

Question 46

Simplify the complex fraction.

A)
B)
C)
D)
E)

Question 47

Combine and simplify.

A)
B)
C)
D)
E)

Question 48

Combine and simplify.

A)
B)
C)
D)
E)

Question 49

Fill in the missing factor.

A)
B)
C)
D)
E)

Question 50

Combine and simplify.

A)
B)
C)
D)
E)

Question 51

Find the least common multiple of the expressions.

A)
B)
C)
D)
E)

Question 52

Find the least common multiple of the expressions.

A)
B)
C)
D)
E)

Question 53

Simplify the complex fraction.

A)
B)
C)
D)
E)

Question 54

Combine and simplify.

A)
B)
C)
D)
E)

Question 55

Combine and simplify.

A)
B)
C)
D)
E)

Question 56

Combine and simplify.

A)
B)
C)
D)
E)

Question 57

Combine and simplify.

A)
B)
C)
D)
E)

Question 58

Combine and simplify.

A)
B)
C)
D)
E)

Question 59

Combine and simplify.

A)
B)
C)
D)
E)

Question 60

Combine and simplify.

A)1,
B)
C)
D)
E)

Question 61

Simplify the complex fraction.

A)
B)
C)
D)
E)

Question 62

Simplify the complex fraction.

A)
B)
C)
D)
E)

Question 63

Simplify the complex fraction.

A)
B)
C)
D)
E)

Question 64

Simplify the complex fraction.

A)
B)
C)
D)
E)

Question 65

Simplify the complex fraction.

A)
B)
C)
D)
E)

Question 66

Simplify the expression.

A)
B)
C)
D)
E)

Question 67

Simplify the complex fraction.

A)
B)
C)
D)
E)

Question 68

Perform the division.

A)
B)
C)
D)
E)

Question 69

Determine the average of the two real numbers and .

A)
B)
C)
D)
E)

Question 70

Simplify the complex fraction.

A)
B)
C)
D)
E)

Question 71

Simplify the complex fraction.

A)
B)
C)
D)
E)

Question 72

Simplify the complex fraction.

A)
B)
C)
D)
E)

Question 73

Perform the division.

A)
B)
C)
D)
E)

Question 74

Simplify the complex fraction.

A)
B)
C)
D)
E)

Question 75

Simplify the complex fraction.

A)
B)
C)
D)
E)

Question 76

Simplify the complex fraction.

A)
B)
C)
D)
E)

Question 77

Perform the division.

A)
B)
C)
D)
E)

Question 78

Simplify the complex fraction.

A)
B)
C)
D)
E)

Question 79

Simplify the expression.

A)
B)
C)
D)
E)

Question 80

Use the function to find and simplify the expression for .

A)
B)
C)
D)
E)