Deck 1: Linear Equations and Functions

Question 1

Solve the equation. ​ ​

A)
B) 28
C)
D)
E) 7

Answer 1

Question 2

The equation in this problem leads to a linear equation. Solve for x. Because the solution to the linear equation may not be a solution to the original equation, be sure to check the solution in the original equation. ​ ​

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

Answer 2

x =

Question 3

Solve for . ​

A)
B)
C)
D)
E)

Answer 3

Question 4

Solve for y in terms of x. ​ ​

A)
B)
C)
D)
E)

Question 5

Use a calculator to solve the equation. Round your answer to three decimal places. ​ ​

A) x = 6.17
B) x = 1.033
C) x = 2.17
D) x = 3.668
E) x = 15.533

Question 6

Solve the equation. ​ ​

A) ​
B)
C) 8
D) 0
E) 2

Question 7

Solve for t. ​

A)
B)
C)
D)
E)

Question 8

Solve the equation. ​ ​

A)
B)
C)
D)
E)

Question 9

The equation in this problem leads to a linear equation. Solve for x. Because the solution to the linear equation may not be a solution to the original equation, be sure to check the solution in the original equation. ​ ​

A) x = 2
B) x = -2
C) x = 4
D) x = 6
E) x =

Question 10

Solve the equation. ​ ​

A) 9
B) 4
C) 5
D) 1
E) 0

Question 11

Solve for y in terms of x. ​ ​

A)
B)
C)
D) ​
E)

Question 12

The equation in this problem leads to a linear equation. Solve for x. Because the solution to the linear equation may not be a solution to the original equation, be sure to check the solution in the original equation. ​ ​

A) x =
B) x =
C) x =
D) x = -20
E) no solution

Question 13

Use a calculator to solve the equation. Round your answer to three decimal places. ​ ​

A) x = 1.639
B) x = 0.61
C) x = -0.779
D) x = -1.284
E) x = -1.397

Question 14

Solve the inequality. ​ ​

A) x < 18
B) x > 18
C) x > -18
D) x < -18
E) x > 14

Question 15

The equation in this problem leads to a linear equation. Solve for x. Because the solution to the linear equation may not be a solution to the original equation, be sure to check the solution in the original equation. ​ ​

A) x = 5
B) x = 15
C) x =
D) x =
E) no solution

Question 16

Solve the equation. ​ ​

A) x = 66
B) ​x =
C) x =
D) x =
E) x = 7

Question 17

Solve the inequality. ​ ​

A)
B)
C)
D)
E)

Question 18

Solve the equation. ​ ​

A)
B)
C)
D)
E)

Question 19

Solve the equation. ​ ​

A) ​-3
B) 36
C) -18
D) 18
E) -6

Question 20

Solve the inequality. ​ ​

A)
B)
C)
D)
E)

Question 21

Dish Systems manufactures satellite systems and has its monthly profit P in dollars related to the number of satellite systems x by . Find the number of systems that Dish Systems needs to produce and sell in order to break even. ​

A) 256 systems
B) 1,080 systems
C) 285 systems
D) 68 systems
E) 270 systems

Question 22

A retired woman has $130,000 to invest. She has chosen one relatively safe investment fund that has an annual yield of 9% and another, riskier one that has an annual yield of 13%. How much should she invest in the fund yielding 9% if she would like to earn $14,000 per year from her investments? ​

A) $11,700
B) $16,900
C) $57,500
D) $72,500
E) $113,100

Question 23

Solve the inequality and choose the graph of the solution. ​ ​

A) ​ ​
B) ​ ​
C) ​ ​
D) ​ ​
E) ​ ​

Question 24

Burnem, Inc. manufactures blank CDs and sells them to a distributor in packs of 500 CDs. Assume Burnem's total cost and total revenue (in dollars) for x packs of 500 CDs are given by ​
Total cost = Total revenue = ​
How many packs of 500 CDs must Burnem sell to break even?
​

A) 490 packs
B) 432 packs
C) 500 packs
D) 387 packs
E) 865 packs

Question 25

The combination of cold temperatures and wind speed determine what is called wind chill. The wind chill is a temperature that is the still-air equivalent of the combination of cold and wind. When the wind speed is 25 mph, the wind chill WC depends on the temperature t (in degrees Fahrenheit) according to . For what temperatures does it feel at least 30°F colder than the air temperature? That is, find t such that . Round your answer to two decimal places. ​ ​

A)
B)
C)
D)
E)

Question 26

Solve the inequality and choose the graph of the solution. ​
​ ​

A) ​ ​
B) ​ ​
C) ​ ​
D) ​ ​
E) ​ ​

Question 27

In Sweetwater, Arizona, water bills are taxed on the basis of the amount of the monthly bill in order to encourage conservation. If the bill is more than $0 but less than $40, the tax is 3% of the bill; if the bill is $40 or more but less than $60, the tax is 5% of the bill; and if the bill is $60 or more, the tax is 7% of the bill. Choose the inequalities that represent the amounts of tax owed in these three cases, where T is the tax to be paid and B is the monthly bill. ​

A) ​If , then
If , then
If , then
B) ​If , then ​
If , then
If , then
​
C) ​If , then
If , then
If , then ​
​
D) ​If , then
If , then
If , then ​
​
E) ​If , then
If , then
If , then
​

Question 28

When a $837,000 building is depreciated for tax purposes (by the straight-line method), its value y after x months of use is given by . How many months will it be before the building is fully depreciated (that is, its value is $0)? ​

A) 37 months
B) 372 months
C) 4 months
D) 27 months
E) 270 months

Question 29

Solve the inequality. ​
​ ​

A)
B)
C)
D)
E)

Question 30

One safe investment pays 10% per year, and a more risky investment pays 18% per year. A woman who has $145,400 to invest would like to have an income of $20,000 per year from her investments. How much should she invest at in the 18% rate fund? ​

A) $77,150
B) $68,250
C) $104,600
D) $83,680
E) $54,600

Question 31

Suppose a professor counts the final exam as being equal to each of the other tests in her course, and she will also change the lowest test score to match the final exam score if the final exam score is higher. If a student's four test scores are 85, 83, 54, and 95, what is the lowest score the student can earn on the final exam and still obtain at least an 80 average for the course? ​

A) 69
B) 83
C) 90
D) 72
E) 84

Question 32

A $670,000 property is depreciated for tax purposes by its owner with the straight-line depreciation method. The value of the building y, after x months of use is given by dollars. After how many months will the value of the building be $339,000? Round your answer to the nearest whole number of months. ​

A) 561 months
B) 372 months
C) 184 months
D) 188 months
E) 377 months

Question 33

For a certain product, the revenue function is and the cost function is . To obtain a profit, the revenue must be greater than the cost. Find the graph of x which shows when there is a profit. ​

A) ​ ​
B) ​ ​
C) ​ ​
D) ​ ​
E) ​ ​

Question 34

Thrifty rents a compact car for $33 per day, and Budget rents a similar car for $21 per day plus an initial fee of $96. Which of the following graphs depicts the number of days for which it would be cheaper to rent from Budget? ​

A) ​ ​
B) ​ ​
C) ​ ​
D) ​ ​
E) ​ ​

Question 35

Solve the inequality and choose the graph of the solution. ​ ​

A) ​ ​
B) ​ ​
C) ​ ​
D) ​ ​
E) ​ ​

Question 36

In wildlife management, the capture-mark-recapture technique is used to estimate the populations of fish or birds in an area or to measure the infestation of insects such as Japanese beetles. Suppose 100 individuals of the species being studied are caught, marked, and released, and one week later 100 more are caught. To estimate the total number of individuals, the following relationship is used: ​ ​
Suppose that 1000 beetles are captured, marked, and released. Suppose further that in the second capture of 1000 it is found that 61 are marked. What is the population estimate?
​

A) 61,000
B) 269
C) 61
D) 16,393
E) 3,721

Question 37

Solve the inequality. ​ ​

A)
B)
C)
D)
E)

Question 38

In seawater, the pressure p is related to the depth d according to , where d is in feet and p is in pounds per square inch. The Titanic was discovered at a depth of 12,460 ft. Find the pressure at this depth. Round your answer to the nearest whole number. ​

A) 6,781 lb/sq in
B) 22,871 lb/sq in
C) 22,816 lb/sq in
D) 6,811 lb/sq in
E) 6796 lb/sq in

Question 39

The total price of a new car (including 5% sales tax) is $28,068. How much of this is tax? Round your answer to the nearest cent. ​

A) $1,333.23
B) $7,484,219.93
C) $2,806.80
D) $2,666.46
E) $1,336.57

Question 40

The percent p of high school seniors who smoke cigarettes can be modeled by the equation , where t is the number of years past 1975. Find the year in which p first becomes negative. Round your answer to the nearest year. ​

A) 2576
B) 2075
C) 2005
D) 4941
E) 2074

Question 41

Let . Find . ​

A)
B) ​
C) ​
D)
E)

Question 42

Let and . Does ?
​

Question 43

If , find . ​

A) 39
B) -15
C) 45
D) -3
E) -21

Question 44

If , is y a function of x?
​

Question 45

Which of the graphs below represent y as a function of x? ​
(a)
​ (b)
​ ​

A) both (a) and (b)
B) neither (a) nor (b)
C) only (b)
D) only (a)

Question 46

If , find . ​

A) 3
B) 15
C) 27
D) -3
E) 45

Question 47

The relation defined by the table is a function. Choose the correct domain and range. ​

A)
B) ​
C)
D)
E)

Question 48

Let and . Find and simplify. ​

A)
B)
C) ​
D)
E) ​

Question 49

Let and . Does for all values of x and h?
​

Question 50

Use the values in the following table. ​

If the function defined by the table is denoted by f, so that is an input or an output of ?
​

A) ​ is an input of 11eca9ac_e341_775e_b76e_1d50da108f2b_TB4005_11
B) ​ is an output of 11eca9ac_e341_775e_b76e_1d50da108f2b_TB4005_11

Question 51

Let . Is ?
​

Question 52

If and , find and simplify. ​

A)
B)
C)
D)
E)

Question 53

If , is y a function of x?

Question 54

Is the relation defined by the table a function of x?

Question 55

If is y a function of x?

Question 56

Which of the graphs below represent y as a function of x? ​
(a)
​ (b)
​ ​

A) only (a)
B) only (b)
C) neither (a) nor (b)
D) both (a) and (b)

Question 57

Is the relation defined by the table a function of x?
​

Question 58

Determine whether the values in the table describe x as a function of y.

Question 59

If , find . ​

A)
B)
C)
D)
E) ​

Question 60

If , find . ​

A) -2
B) 0
C) -2000
D) -200
E) 100

Question 61

Find the domain and range of the function below. ​ ​

A) domain: real numbers
Range: real numbers
B) domain: real numbers
Range: real numbers
C) domain: all reals
Range: real numbers
D) domain: real numbers
Range: real numbers
E) domain: all reals
Range: real numbers

Question 62

Find the domain and range of the function below. ​ ​

A) domain: all reals
Range: real numbers
B) domain: all reals
Range: real numbers
C) domain: real numbers
Range: all reals
D) domain: real numbers
Range: all reals
E) domain: all reals
Range: real numbers

Question 63

The graph of is shown in the figure below. ​ ​
If the point P (with coordinates (a, b)) is on the graph, how are a and b related?
​

A) ​
B)
C)
D)
E) There is no relation.

Question 64

For and , find . ​

A)
B)
C)
D)
E)

Question 65

For and , find . ​

A)
B)
C)
D)
E)

Question 66

For and , find . ​

A)
B)
C)
D)
E)

Question 67

For and , find . ​

A)
B)
C)
D)
E)

Question 68

If and , find and simplify. ​

A) ​
B)
C)
D) ​
E)

Question 69

A function and its graph are given. Find the domain. ​ ​ ​

A) domain: all real numbers
B) domain: all real numbers
C) domain: all real numbers
D) domain: all real numbers
E) domain: all real numbers

Question 70

For and , find . ​

A)
B) ​
C)
D)
E)

Question 71

When a debt is refinanced, sometimes the term of the loan (that is, the time it takes to repay the debt) is shortened. Suppose the current interest rate is 7%, and the current debt is $100,000. The monthly payment R of the refinanced debt is a function of the term of the loan t in years. If we represent this function by , then the following table defines the function. ​

​
Source: Comprehensive Mortgage Payment Tables, Publication No. 492, Financial Publishing Co., Boston
Choose the correct verbal description of .
​

A) From the table, the value of is the yearly payment to repay a $100,000 loan in 12 years when the interest rate is 7%.
B) From the table, the value of is the monthly payment to repay half of a $100,000 loan in 12 years when the interest rate is 7%.
C) From the table, the value of is the weekly payment to repay a $100,000 loan in 12 years when the interest rate is 7%.
D) From the table, the value of is the monthly payment to repay a $100,000 loan in 12 years when the interest rate is 7%.
E) From the table, the value of is the monthly payment to repay a $100,000 loan in 12 years when the interest rate is 7%.

Question 72

A function and its graph are given. Find the domain. ​ ​ ​
​

A) domain:
B) domain:
C) domain:
D) domain:
E) domain:

Question 73

A couple seeking to buy a home decides that a monthly payment of $800 fits their budget. Their bank's interest rate is 7.5%. The amount they can borrow A is a function of the time t in years that it will take to repay the debt. If we denote this function by , then the following table defines the function. ​

Source: Comprehensive Mortgage Payment Tables, Publication No. 492, Financial Publishing Co., Boston
Choose the expression in the form which describes how long they will have to make payments if they need to borrow $103,000.
​

A)
B)
C) ​
D)
E) ​

Question 74

If t represents the number of hours after 9:30 A.M. on Tuesday, October 5, 2004, then the graph defines the Dow Jones Industrial Average D as a function of time t. If we represent this function by use the graph to find f(6.5). ​ ​

A) 10,160
B) 10,175
C) 10,190
D) 10,217
E) 10,220

Question 75

Suppose in the figure below. Find . ​
​ ​

A) 1.44225
B) 1
C) -1.414214
D) 0
E) 1.414214

Question 76

For and , find . ​

A)
B)
C)
D)
E)

Question 77

For , find . ​

A) 1
B) ​
C)
D) ​
E) x

Question 78

Suppose in the figure below. How many values of x satisfy ? ​ ​

A) 2
B) 1
C) 3
D) 5
E) 4

Question 79

State the domain and range of the function below. ​ ​

A) domain: real numbers
Range: real numbers
B) domain: all reals
Range: real numbers
C) domain: real numbers
Range: all reals
D) domain: all reals
Range: real numbers
E) domain: real numbers
Range: real numbers

Question 80

The graph of is shown in the figure below.
​
​ ​
Does the point (2,2) lie on the graph? In other words, do the coordinates satisfy the equation?
​