Deck 5: Rational Expressions, Equations and Functions

Question 1

Find any real boundary values for each rational inequality.

-

A)
B)
C)
D)
E) none of these

Answer 1

Question 2

Find any real boundary values for each rational inequality.

-

A)
B)
C)
D)
E) none of these

Answer 2

Question 3

Find any real boundary values for each rational inequality.

-

A)
B)
C)
D)
E) none of these

Answer 3

Question 4

Use interval notation to represent the number line graph.

-

A)
B)
C)
D)
E) none of these

Question 5

Use interval notation to represent the number line graph.

-

A)
B)
C)
D)
E) none of these

Question 6

Use interval notation to represent the number line graph.

-

A)
B)
C)
D)
E) none of these

Question 7

Use interval notation to represent the number line graph.

-

A)
B)
C)
D)
E) none of these

Question 8

Use the rational inequality .

-Find any real boundary values.

A)
B)
C)
D)
E) none of these

Question 9

Use the rational inequality .

-Use interval notation to represent the solution.

A)
B)
C)
D)
E) no solution

Question 10

Use the rational inequality .

-Find any real boundary values.

A)
B)
C)
D)
E) none of these

Question 11

Use the rational inequality .

-Use interval notation to represent the solution.

A)
B)
C)
D)
E) no solution

Question 12

Use the rational inequality

-Find any real boundary values.

A)
B)
C)
D)
E) none of these

Question 13

Use the rational inequality

-Use interval notation to represent the solution.

A)
B)
C)
D)
E) no solution

Question 14

Use the rational inequality

-Find any real boundary values.

A)
B)
C)
D)
E) none of these

Question 15

Use the rational inequality

-Use interval notation to represent the solution.

A)
B)
C)
D)
E) no solution

Question 16

Simplify the expression.

-

A)
B)
C)
D)
E) none of these

Question 17

Simplify the expression.

-

A)
B)
C)
D)
E) none of these

Question 18

Simplify the expression.

-

A)
B)
C)
D)
E) none of these

Question 19

Use long division to find the quotient.

-

A)
B)
C)
D)
E) none of these

Question 20

Use long division to find the quotient.

-

A)
B)
C)
D)
E) none of these

Question 21

Use long division to find the quotient.

-

A)
B)
C)
D)
E) none of these

Question 22

Use long division to find the quotient.

-

A)
B)
C)
D)
E) none of these

Question 23

Use long division to find the quotient.

-

A)
B)
C)
D)
E) none of these

Question 24

Use long division to find the quotient.

-

A)
B)
C)
D)
E) none of these

Question 25

Use synthetic division to find the quotient.

-

A)
B)
C)
D)
E) none of these

Question 26

Use synthetic division to find the quotient.

-

A)
B)
C)
D)
E) none of these

Question 27

Use synthetic division to find the quotient.

-

A)
B)
C)
D)
E) none of these

Question 28

Use synthetic division to find the quotient.

-

A)
B)
C)
D)
E) none of these

Question 29

Use the remainder theorem to determine which, if any, of these binomials are factors of

A)
B)
C)
D)
E) none of these

Question 30

Use synthetic division to find the quotient and the remainder theorem to evaluate the function At

A)
B)
C)
D)
E) none of these

Question 31

Use synthetic division to find the quotient and the remainder theorem to evaluate the function At

A)
B)
C)
D)
E) none of these

Question 32

The relationship of the input value, x , and the output value, y , is a direct variation. When x = 5 , y =25 .

-Write a function that describes this direct variation and graph it.

A)
B)
C)
D)
E) none of these

Question 33

The relationship of the input value, x , and the output value, y , is a direct variation. When x = 5 , y =25 .

-Use the graph to find y when x = 1 .

A) 0
B)
C) 5
D) 25
E) none of these

Question 34

The relationship of the input value, , and the output value, , is an inverse variation. When ,
.

-Write a function that describes this inverse variation and graph the function.

A)
B)
C)
D)
E) none of these

Question 35

The relationship of the input value, , and the output value, , is an inverse variation. When ,
.

-Use the graph to find y when x = 4 .

A) 2
B) 8
C) 10
D) 4
E) none of these

Question 36

The relationship between the cost, , of purchasing chocolate-covered almonds and the weight, , in pounds is a direct variation. The cost of purchasing 4 pounds of almonds is $38.00.

-Find the constant of proportionality.

A)
B)
C)
D)
E) none of these

Question 37

The relationship between the cost, , of purchasing chocolate-covered almonds and the weight, , in pounds is a direct variation. The cost of purchasing 4 pounds of almonds is $38.00.

-Find the cost of purchasing 5 pounds.

A) $50.50
B) $51.50
C) $47.50
D) $45.50
E) none of these

Question 38

The relationship between the velocity of a falling object (ignoring air resistance) , and the time of the fall , is a direct variation. When the velocity of the object is 210 feet per second, it has been falling for 6 seconds. Find the constant of proportionality. Include units of measurement.

A)
B)
C)
D)
E) none of these

Question 39

The relationship between the velocity of a falling object (ignoring air resistance) , and the time of the fall , is a direct variation. When the velocity of the object is 64 feet per second, it has been falling for 2 seconds. What will the object's velocity be after 3 seconds?

A)
B)
C)
D)
E) none of these

Question 40

The relationship between the time it takes you to drive to school, , and your average speed, in miles per hour is an inverse variation. It takes 0.5 hours to get to school when your average speed is .

-Find the constant of proportionality. Include units of measurements.

A)
B)
C)
D)
E) none of these

Question 41

The relationship between the time it takes you to drive to school, , and your average speed, in miles per hour is an inverse variation. It takes 0.5 hours to get to school when your average speed is .

-At what speed do you need to be going to travel this distance in 0.75 hrs?

A)
B)
C)
D)
E) none of these

Question 42

The relationship between the current, , in a circuit, measured in amperes and its resistance, , measured in ohms, is an inverse variation. When the current in the circuit is 26 amperes, the resistance is 3 ohms.Find the constant of proportionality. Include units of measurements.

A)
B)
C)
D)
E) none of these

Question 43

A joint variation is . If , and , find . Round your answer to two decimal places.

A) 48
B) 0.75
C) 1.3
D) 8
E) none of these

Question 44

A combined variation is . If , and , find
.

A) 21.3
B) 15
C) 7.5
D) 12
E) none of these

Question 45

Solve the formula for
.

A)
B)
C)
D)
E) none of these

Question 46

Solve the formula for
.

A)
B)
C)
D)
E) none of these

Question 47

Use interval notation to represent the domain of each function.

-

A)
B)
C)
D)
E) none of these

Question 48

Use interval notation to represent the domain of each function.

-

A)
B)
C)
D)
E) none of these

Question 49

Use interval notation to represent the domain of each function.

-

A)
B)
C)
D)
E) none of these

Question 50

Use interval notation to represent the domain of each function.

-

A)
B)
C)
D)
E) none of these

Question 51

Use interval notation to represent the domain of each function.

-

A)
B)
C)
D)
E) none of these

Question 52

write the equation of any vertical asymptotes.

-

A)
B)
C)
D) no vertical asymptotes
E) none of these

Question 53

write the equation of any vertical asymptotes.

-

A)
B)
C)
D) no vertical asymptotes
E) none of these

Question 54

write the equation of any vertical asymptotes.

-

A)
B)
C)
D) no vertical asymptotes
E) none of these

Question 55

Identify the location of any holes on the graph of the function.

-

A)
B)
C)
D) no holes
E) none of these

Question 56

Identify the location of any holes on the graph of the function.

-

A)
B)
C)
D) no holes
E) none of these

Question 57

Find
for the function

.

A)
B) 0
C)
D) undefined
E) none of these

Question 58

Use an algebraic method to find any real zeros, if they exist, of the function
.

A)
B)
C)
D) no real zeros
E) none of these

Question 59

Use an algebraic method to find any real zeros, if they exist, of the function
.

A)
B)
C)
D) no real zeros
E) none of these

Question 60

A company wants to collect $299,000 from selling a particular product. The relationship of the number of products sold, , and the product price, , is . The company predicts that 23,000 products will be sold. Find the product price.

A) $15
B) $17
C) $13
D) $18
E) none of these

Question 61

The installation and setup fees for installing a new home security system total $500. It costs $360 per year to manage the system. The average annual cost, in dollars, , to use the system for years is
. Find the average annual cost of using this system for 4 years.

A) $860
B) $495
C) $585
D) $485
E) none of these

Question 62

A)
B)
C)
D)
E) no solution

Question 63

A)
B)
C)
D)
E) no solution

Question 64

A)
B)
C)
D)
E) no solution

Question 65

A)
B)
C)
D)
E) no solution

Question 66

A)
B)
C)
D)
E) no solution

Question 67

A)
B)
C)
D)
E) no solution

Question 68

A)
B)
C)
D)
E) no solution

Question 69

A)
B)
C)
D)
E) no solution

Question 70

A)
B)
C)
D)
E) no solution

Question 71

A)
B)
C)
D)
E) no solution

Question 72

If a household of 6 people produces 168 pounds of garbage in one week, at this same rate, how many pounds will 42 people produce in one week?

A) 24 lbs
B) 7056 lbs
C) 1216 lbs
D) 1176 lbs
E) none of these

Question 73

If 150 grams of ice cream contains 17 grams of fat, how much fat is in 390 grams of ice cream? Round your answer to the nearest tenth.

A) 1.7 g
B) 3441.2 g
C) 44.2 g
D) 140 g
E) none of these

Question 74

Lisa can paint the interior of a 1000 square-foot house in 11 hours by herself. Liam can paint the same size house in 14 hours by himself. How long will it take to paint the same size house if they work together? Round your answer to the nearest hour.

A) 6 hrs
B) 12.5 hrs
C) 4 hrs
D) 8 hrs
E) none of these

Question 75

A swimming pool can be emptied in 4 hours using two pumps--a 10-horsepower pump along with a 6-horsepower pump. The 6-horsepower pump takes 6 more hours than the 10-horsepower pump to empty the pool alone. How long would it take the 10-horsepower pump to empty the pool alone?

A) 9 hrs
B) 7 hrs
C) 6 hrs
D) 8 hrs
E) none of these

Question 76

In a parallel circuit with two resistors, the total resistance is calculated using the formula . The total resistance in the circuit is , the resistance of one resistor is and the resistance of the other resistor is . The unit of measure of resistance is ohms. If a parallel circuit has a total resistance of 6 ohms and one of the resistors in the circuit is 18 ohms, find the resistance of the other resistor.

A) 9 ohms
B) 4.5 ohms
C) 54 ohms
D) 7 ohms
E) none of these

Question 77

Evaluate or simplify each expression.

-

A)
B)
C)
D)
E) none of these

Question 78

Evaluate or simplify each expression.

-

A)
B)
C)
D)
E) none of these

Question 79

Evaluate or simplify each expression.

-

A)
B)
C)
D)
E) none of these

Question 80

Evaluate or simplify each expression.

-

A)
B)
C)
D)
E) none of these