Title: Unit 3 Quiz
Course: Technical Math for Industry

Q: To form 3 adjacent squares (as in the figure), 10 toothpicks are required. How many toothpicks are required to form 100 adjacent squares?
- 301 (Correct. Notice that each new square requires 3 more toothpicks (2 horizontal and 1 vertical). Since we need 97 more squares (starting at the given figure), 100 squares will require , which equals 301 toothpicks.)
- 300 (Incorrect. Try a smaller number of squares first (4 and 5, for example). Do you see in a pattern in the number of toothpicks required? How many "new" toothpicks are required when you add an additional square? How many additional squares need to be added to the given figure in order to get 100 squares?)
- 107 (Incorrect. Try a smaller number of squares first (4 and 5, for example). Do you see in a pattern in the number of toothpicks required? How many "new" toothpicks are required when you add an additional square? How many additional squares need to be added to the given figure in order to get 100 squares?)
- 251 (Incorrect. Try a smaller number of squares first (4 and 5, for example). Do you see in a pattern in the number of toothpicks required? How many "new" toothpicks are required when you add an additional square? How many additional squares need to be added to the given figure in order to get 100 squares?)
A: 301

Q: For which of the following sequences is it true that every term (after the first one) is 4 less than the previous term?
- 7, 3, -1, -5, ... (Correct. Every term is 4 less than the term before it (7 - 4 = 3, 3 - 4 = -1, - 1- 4 = -5).)
- 9, 5, 1, 3, ... (Incorrect. The fourth term is 2 more than the third term (NOT 4 less than the third term), so the sequence does not match the description.)
- -3, 1, 5, 9, ... (Incorrect. Each term after the first one is 4 MORE than the one before it, so the sequence does not match the description.)
- 8, 4, 8, 4, ... (Incorrect. The third term is 4 more than the second term (NOT 4 less than the second term), so the sequence does not match the description.)
A: 7, 3, -1, -5, ...

Q: Use inductive reasoning to find the 10th term in the sequence 5, 8, 11, 14, ...
- 32 (Correct. Since each term is 3 more than the one before it, to determine the 10th term, you can start with the 4th term, which is 14, then add 3 a total of six times.)
- 17 (Incorrect. What is the difference between the first two numbers? The next two? If this pattern continues, how can you get from the 4th term to the 10th term? How many times do you need to add 3?)
- 34 (Incorrect. What is the difference between the first two numbers? The next two? If this pattern continues, how can you get from the 4th term to the 10th term? How many times do you need to add 3?)
- 50 (Incorrect. What is the difference between the first two numbers? The next two? If this pattern continues, how can you get from the 4th term to the 10th term? How many times do you need to add 3?)
A: 32

Q: Since Jacob's family moved to a house near where his grandparents live, his grandmother and grandfather have visited every Sunday afternoon. The first week, they gave him 15 books and every Sunday since then, they have brought 4 more books. After their tenth visit, how many books had Jacob grandparents brought him?
- 51 (Correct. Each Sunday after the first one, Jacob received 4 more books, so to determine the number of books he has after ten visits, we need to add 4 a total of 9 times to 15 (the initial number of quarters). After his grandparents' sixth visit, Jacob will have received a total of 15 + 4(9) (which equals 51) comic books.)
- 150 (Incorrect. After the first group of 7 books, Jacob receives 4 more each week. How many additional groups of 4 books will Jacob have received by his grandparents' 10th visit?)
- 27 (Incorrect. After the first group of 7 books, Jacob receives 4 more each week. How many additional groups of 4 books will Jacob have received by his grandparents' 10th visit?)
- 60 (Incorrect. After the first group of 7 books, Jacob receives 4 more each week. How many additional groups of 4 books will Jacob have received by his grandparents' 10th visit?)
A: 51

Q: In a certain sequence, the first term equals 24 and each term after the first is times the term before it. What is the 4th term of this sequence?
- 12 (Incorrect. If the first term is 24, what must the second term equal? Remember that each term is times the one before it. Continue this pattern to determine the 4th term.)
- 192 (Incorrect. If the first term is 24, what must the second term equal? Remember that each term is times the one before it. Continue this pattern to determine the 4th term.)
- 3 (Correct. Since the first term is 24, the second term is , which equals 12, and the third term is , which equals 6, so the fourth terms is which equals 3.)
- 6 (Incorrect. If the first term is 24, what must the second term equal? Remember that each term is times the one before it. Continue this pattern to determine the 4th term.)
A: 3

Q: A common mathematical pattern starts as 1, 1, 2, 3, 5, ... The first two terms are both equal to 1 and after that, each number in the sequence is the sum of the two numbers immediately before it. That is, the third term in the sequence is 2 (since that equals 1 + 1), the fourth term is 3 (since that equals 1 + 2), and the fifth term must be 2 + 3, which equals 5. Therefore, the first five terms in the sequence (called the "Fibonacci Sequence") are 1, 1, 2, 3, and 5.  What is the 12th term of the sequence?
- 89 (Incorrect. Recall that the first five terms of the sequence are 1, 1, 2, 3, and 5, so the 6th term must equal 3 + 5, which is 8, and the 7th term is 5 + 8, which equals 13. Now we know the first 7 terms are 1, 1, 2, 3, 5, 8, 13. Can you continue the process to find the 12th term of the sequence?)
- 34 (Incorrect. Recall that the first five terms of the sequence are 1, 1, 2, 3, and 5, so the 6th term must equal 3 + 5, which is 8, and the 7th term is 5 + 8, which equals 13. Now we know the first 7 terms are 1, 1, 2, 3, 5, 8, 13. Can you continue the process to find the 12th term of the sequence?)
- 233 (Incorrect. Recall that the first five terms of the sequence are 1, 1, 2, 3, and 5, so the 6th term must equal 3 + 5, which is 8, and the 7th term is 5 + 8, which equals 13. Now we know the first 7 terms are 1, 1, 2, 3, 5, 8, 13. Can you continue the process to find the 12th term of the sequence?)
- 144 (Correct. Knowing that the first 5 terms of the sequence are 1, 1, 2, 3, and 5, the 6th term must equal 3 + 5 = 8, the 7th term is 5 + 8 = 13, the 8th term is 8 + 13 = 21, the 9th term is 13 + 21 = 34, 10th term is 21 + 34 = 55, the 11th term is 34 + 55 = 89, and therefore the 12th term is 55 + 89 = 144.)
A: 144

Q: Based on the numbers in this table, which equation describes the value of y in terms of x?

x | y
1 | 3
2 | 6
3 | 11
4 | 18
A: (a choice with no text)
If right: Correct. For every row in the table, the value of y is 2 more than , where x is the associated x value (that is, ).
If wrong: Incorrect. Check that for every row in the table the value of y is found by evaluating the expression using the value of x.
If wrong: Incorrect. Check that for every row in the table the value of y is found by evaluating the expression using the value of x.
If wrong: Incorrect. Check that for every row in the table the value of y is found by evaluating the expression using the value of x.

Q: Which table matches the graph below?
- x | y
1 | 1
2 | 1.5
3 | 2
4 | 2.5 (Incorrect. Check that the x-y pairs in each row of the table correspond to (x, y) points on the graph. Remember that the horizontal axis is represented by the x value.)
- x | y
1 | 1.5
2 | 2
3 | 2.5
4 | 3 (Correct. The points (1, 1.5), (2, 2), (3, 2.5), and (4, 3) are each points on the graph.)
- x | y
1 | 2
2 | 3
3 | 4
4 | 6 (Incorrect. Check that the x-y pairs in each row of the table correspond to (x, y) points on the graph. Remember that the horizontal axis is represented by the x value.)
- x | y
1 | 0
2 | 2
3 | 4
4 | 6 (Incorrect. Check that the x-y pairs in each row of the table correspond to (x, y) points on the graph. Remember that the horizontal axis is represented by the x value.)
A: x | y
1 | 1.5
2 | 2
3 | 2.5
4 | 3

Q: Which of the following tables represents the equation ?
- x | y
1 | 5
2 | 8
3 | 11
4 | 14
5 | 17 (Incorrect. In order for the table to represent the equation, each y value in a row must equal 8 more than negative three times the corresponding x value.)
- x | y
1 | 3
2 | 5
3 | 7
4 | 9
5 | 11 (Incorrect. In order for the table to represent the equation, each y value in a row must equal 8 more than negative three times the corresponding x value.)
- x | y
1 | 11
2 | 14
3 | 17
4 | 20
5 | 23 (Incorrect. In order for the table to represent the equation, each y value in a row must equal 8 more than negative three times the corresponding x value.)
- x | y
1 | 5
2 | 2
3 | -1
4 | -4
5 | -7 (Correct. In each row of the table, the y value equals 8 more than negative three times the corresponding x value.)
A: x | y
1 | 5
2 | 2
3 | -1
4 | -4
5 | -7

Q: Which table accurately describes the points shown on the following graph?
- x | y
1 | 2
2 | 3
3 | 4
4 | 1
5 | 0 (Correct. The x, y pairs in the table represent each of the (x, y) points shown in the graph ((1,2), (2,4), (3,1), (4,3), and (5,1)).)
- x | y
1 | 4
2 | 1
3 | 1
4 | 3
5 | 5 (Incorrect. Check to be sure that every (x, y) pair in a row corresponds to a point on the graph. Also, remember that the horizontal axis represents the independent variable, x.)
- x | y
1 | 2
2 | 3
3 | 4
4 | 1
5 | 1 (Incorrect. Check to be sure that every (x, y) pair in a row corresponds to a point on the graph. Also, remember that the horizontal axis represents the independent variable, x.)
- x | y
1 | 4
2 | 1
3 | 2
4 | 3
5 | 0 (Incorrect. Check to be sure that every (x, y) pair in a row corresponds to a point on the graph. Also, remember that the horizontal axis represents the independent variable, x.)
A: x | y
1 | 2
2 | 3
3 | 4
4 | 1
5 | 0

Q: To form Figure 1, 6 toothpicks are required, while Figure 2 requires 11 toothpicks.

Which table represents the relationship between x and y, where y is the number of toothpicks required to build Figure x?
- x | y
1 | 6
2 | 11
3 | 18
4 | 24 (Incorrect. For the table to represent the situation, in each row of the table the y value must equal the number of toothpicks required to form Figure x.)
- x | y
1 | 6
2 | 11
3 | 16
4 | 20 (Incorrect. For the table to represent the situation, in each row of the table the y value must equal the number of toothpicks required to form Figure x.)
- x | y
1 | 6
2 | 11
3 | 16
4 | 21 (Correct. The number of toothpicks required to form Figure 3 is 16 and Figure 4 requires 21 toothpicks; in each row of this table the y value equals the number of toothpicks required to form Figure x.)
- x | y
1 | 6
2 | 11
3 | 16
4 | 24 (Incorrect. For the table to represent the situation, in each row of the table the y value must equal the number of toothpicks required to form Figure x.)
A: x | y
1 | 6
2 | 11
3 | 16
4 | 21

Q: Do the following ordered pairs correspond to a function? {(2,3), (2,4), (3,5), (4,6), (5,7)}
- No. (Correct. These ordered pairs cannot correspond to a function since the x-value 2 corresponds to two different y-values (3 and 4).)
- Yes. (Incorrect. An output (y-value) can occur more than once, but an input (x-value) cannot correspond to more than one output. In this case, the input 2 corresponds to two different outputs (3 and 4), so the ordered pairs do not represent a function.)
A: No.

Q: Does the following graph represent a function?
- No. (Correct. Some x-values (for example, x=-3) correspond to more than one y-value.)
- Yes. (Incorrect. Some x-values (for example, x=-3) correspond to more than one y-value.)
A: No.

Q: Does the graph below represent a function?
- Yes. (Incorrect. Since the graph contains a vertical line segment when x=-1.5, there are many corresponding y-values. What does thos mean?)
- No. (Correct. The graph contains a vertical line segment. When x=-1.5, there are many corresponding y-values.)
A: No.

Q: Does the following table represent a function?

x | y
-1 | 2
1 | 2
3 | 5
5 | 2
- Yes. (Correct. Every x-value corresponds to only one y-value. It is OK that the y-value of 2 corresponds to more than one x-value.)
- No. (Incorrect. Every x-value corresponds to only one y-value. It is acceptable that the y-value of 2 corresponds to more than one x-value.)
A: Yes.

Q: Which set of ordered pairs represents the table?

x | y
1 | 3
2 | 4
3 | 4
5 | 3
- (1,3), (2,4), (3,4), (5,3) (Correct. Each (x,y) pair appears in the table and every row in the table is represented as an ordered pair.)
- (1,3), (2,4), (3,4), (5,3), (5,4) (Incorrect. This set of ordered pairs does not represent the table since the pair (5,4) does not appear in any row of the table.)
- (1,3), (2,4), (3,4), (5,3), (3,5) (Incorrect. This set of ordered pairs does not represent the table since the pair (3,5) does not appear in any row of the table.)
- (3,1), (4,2), (4,3), (3,5) (Incorrect. Remember that an ordered pair represents (x,y) (that is the x-value is on the left).)
A: (1,3), (2,4), (3,4), (5,3)

Q: Referring to Figures A and B, which graphs represent functions?
- Only Figure B. (Incorrect. Figure B does represent a function, because for every input (x) value, there is exactly one defined output (y) value. The gap in the line (between x= 0 and x=3) does not preclude this from being a function; the function is just undefined here. Are multiple y-values defined for any x-value in Figure A?)
- Neither Figure A nor Figure B. (Incorrect. At least one of the graphs represents a function. Remember, for a graph to represent a function, every input (x-value) corresponds to exactly one output (y-value).)
- Only Figure A. (Incorrect. Figure A does represent a function, because for every input (x) value, there is exactly one defined output (y) value. Are multiple y-values defined for any x-value in Figure B?)
- Both Figure A and Figure B. (Correct. Both figures are examples of functions. Figure A represents a function because for every input (x) value, there is exactly one defined output (y) value. Figure B represents a function also, because for every input (x) value, there is exactly one defined output (y) value. The gap in the line (between x= 0 and x=3) does not preclude this from being a function; the function is just undefined here.)
A: Both Figure A and Figure B.

Q: The table of a function is shown below. What is its domain?

x | y
-1 | 4
0 | 1
2 | 3
4 | 3
5 | 2
- All real numbers. (Incorrect. The table only lists the 5 input values -1, 0, 2, 4, and 5.)
- {1, 2, 3, 4} (Incorrect. The set {1,2,3,4} actually represents the range of this function.)
- {-1, 0, 2, 4, 5} (Correct. The domain is the collection of x-values given in the table, which is {-1, 0, 2, 4, 5}.)
- The real numbers between -1 and 5. (Incorrect. There are only 5 rows and there are infinitely many real numbers between -1 and 5.)
A: {-1, 0, 2, 4, 5}

Q: The graph of a function is shown below. What is its range?
- All real numbers. (Incorrect. There are only 4 points shown in the graph.)
- {1, 2, 3, 4} (Incorrect. 3 is not an independent value shown on the graph.)
- {1, 2, 4} (Correct. The dependent values shown in the graph are 1, 2, and 4.)
- {1, 2, 3, 5} (Incorrect. This is the domain of the function defined by the graph. 5 and 3 are not dependent values shown in the graph and 4 is a dependent value, but is not included in {1, 2, 3, 5}.)
A: {1, 2, 4}

Q: The three figures below define a function with the figure number as the independent value and the number of toothpicks required to construct each figure as the dependent value.

If the domain is {1, 2, 3, 4, ...}, which of the following represents the range of the function?
- {6, 11, 16, 21} (Incorrect. The range will have more than 4 numbers in it.)
- {6, 11, 16, 22} (Incorrect. The range will have more than 4 numbers in it. Also, figure 4 requires 21 toothpicks, so the second element listed in the range should be 21.)
- {6, 11, 16, 21, ...} (Correct. {6, 11, 16, 21, ...} is the correct answer since these values represent all of the outputs of the function.)
- {6, 11, 16, 22, ...} (Incorrect. Figure 4 requires 21 toothpicks, so the fourth element listed in the range should be 21.)
A: {6, 11, 16, 21, ...}

Q: The graph of a function is shown below. The domain of the function is the set of real numbers between -5 and 5. What is the range of the function?
- The real numbers between -3 and 4. (Correct. The y-values on the graph get as low as -3 and as high as 4, taking on all the values in between.)
- The real numbers between -2 and -3. (Incorrect. Notice that there are y-values on the graph that are greater than -2.)
- All real numbers. (Incorrect. Since the domain is the set of real numbers between -5 and 5, the range is the set of y-values that are visible on the graph.)
- The real numbers between -2 and 4. (Incorrect. Notice that there are y-values on the graph that are as low as -3.)
A: The real numbers between -3 and 4.

Q: The graph below represents y as a function of x. Which statement is true about the value 5?
- 5 is in the domain of the function, but is not in the range of the function. (Correct. 5 is one of the x-values shown in the graph, but is not on the y-values.)
- 5 is not in the domain and is not in the range of the function. (Incorrect. 5 does appear as an x-value in this graph.)
- 5 is in the range of the function, but is not in the domain of the function. (Incorrect. 5 is not one of the y-values shown in the graph.)
- 5 is in both the domain and the range of the function. (Incorrect. 5 is not one of the y-values shown in the graph.)
A: 5 is in the domain of the function, but is not in the range of the function.

Q: The table below represents y as a function of x. Which of the following statements is true about the value 0?

x | y
-1 | 0
0 | 1
2 | 3
4 | 4
5 | 7
- 0 is in both the domain and the range of the function. (Correct. 0 appears as both an x-value and a y-value in the table, so 0 is in both the domain and the range of the function.)
- 0 is in the range of the function, but is not in the domain of the function. (Incorrect. 0 appears as a y-value in the table and so 0 is in the range of the function.)
- 0 is in the domain of the function, but is not in the range of the function. (Incorrect. 0 appears as a y-value in the table and so 0 is in the range of the function.)
- 0 is in neither the domain nor the range of the function. (Incorrect. 0 appears as both an x-value and a y-value in the table, so 0 is in both the domain and the range of the function.)
A: 0 is in both the domain and the range of the function.

Q: The function is a proportional function.   True or False?
- True. (Correct. The function is equal to so every value is equal to times the corresponding value, so the function is proportional.)
- False. (Incorrect. Is there one value that you can multiply every x term by to get a corresponding y term? What does that tell you?)
A: True.

Q: Sophie's favorite homemade cookie recipe requires 1 cup of chocolate chips for 12 servings. If the number of cups required for multiple batches is proportional to the number of servings being made, how many cups of chocolate chips will she need to make enough cokies for 24 servings?
- 3 (Incorrect. The relationship is proportional, and she is doubling the number of servings. She also has to double the amount of chocoalte chips that she uses.)
- 2 (Correct. The relationship is proportional; if she doubles the number of servings, then she also has to double the amount of chocoalte chips.)
- 4 (Incorrect. The relationship is proportional, and she is doubling the number of servings. She also has to double the amount of chocoalte chips that she uses.)
- 1 (Incorrect. The relationship is proportional, and she is doubling the number of servings. She also has to double the amount of chocoalte chips that she uses.)
A: 2

Q: The table shows one (x, y) pair for a proportional function. What is the constant of proportionality?

x | y
4 | 3
- Not enough information is given to determine the constant of proportionality. (Incorrect. Since the function is proportional, . Then , which is the constant of proportionality.)
- 4 (Incorrect. Since the function is proportional, . Then , which is the constant of proportionality.)
- 3 (Incorrect. Since the function is proportional, . Then , which is the constant of proportionality.)
A: (a choice with no text)
If right: Correct. Since the function is proportional, . Then , which is the constant of proportionality.

Q: If a function is proportional, what must the corresponding y-value equal when ?
- 1 (Incorrect. Think about some proportional functions, like and . When , what is the value of y?)
- -1 (Incorrect. Think about some proportional functions, like and . When , what is the value of y?)
- 0 (Correct. If the function is proportional, then its equation must be of the form for some constant k. Therefore, when x=0, y equals k times 0, which equals 0.)
- There is not enough information to answer this problem. (Incorrect. Think about some proportional functions, like and . When , what is the value of y?)
A: 0

Q: The graphs of two functions are shown below. Which of these functions are proportional?
- Only Graph A. (Incorrect. This answer is incorrect. When x is positive, each y-value on the graph is 1 times the corresponding x-value, but when x is negative, each y value is -1 times the corresponding x-value, so the function is not proportional.)
- Both Graph A and Graph B. (Incorrect. This answer is incorrect. When x is positive, each y-value on the graph is 1 times the corresponding x-value, but when x is negative, each y value is -1 times the corresponding x-value, so the function shown in Graph A is not proportional.)
- Only Graph B. (Correct. This answer is correct. Graph B represents the function , which is proportional.)
- Neither graph. (Incorrect. This answer is incorrect. Graph B represents the function , which is proportional.)
A: Only Graph B.

Q: A bathtub is being drained so that a linear function describes the amount of water in the tub after x minutes. The tub held 15 gallons before it was drained and it took 20 minutes to empty. At what rate is the tub being drained?
- 20 gallons per minute (Incorrect. Since the function is linear, the number of gallons drained per minute (the function's rate of change) is constant. If 15 gallons are drained in 20 minutes, then you can represent this as the fraction . What fraction does this simplify to?)
- gallons per minute (Correct. Since the function is linear, the number of gallons drained per minute (the function's rate of change) is constant. If 15 gallons are drained in 20 minutes, then 3 gallons will drain in 4 minutes, and therefore in one minute, of a gallon will be drained.)
- gallons per minute (Incorrect. Since the function is linear, the number of gallons drained per minute (the function's rate of change) is constant. If 15 gallons are drained in 20 minutes, then you can represent this as the fraction . What fraction does this simplify to?)
- None of the above. (Incorrect. Since the function is linear, the number of gallons drained per minute (the function's rate of change) is constant. If 15 gallons are drained in 20 minutes, then you can represent this as the fraction . What fraction does this simplify to?)
A: gallons per minute

Q: Jean gets an allowance of $15 each month plus an extra $2 for each chore she completes around the house. How much allowance will she earn if she does chores in a month?
- dollars (Correct. Jean earns 15 dollars plus an additional $2 for each chore she completes, so she will earn dollars for completin g tasks.)
- dollars (Incorrect. Even though this equation gives the right answer when , the amount per chore is incorrect.)
- dollars (Incorrect. If Jean completes 0 chores, she will earn $15, not $2.)
- dollars (Incorrect. The equation correctly shows that Jean earns $2 per chore, but fails to include the fact that she gets $15 per month without having to complete any chores.)
A: dollars

Q: Sophie gets an allowance of $15 each month plus an extra $2 for each chore she completes around the house. Which of the following statements is correct about the amount of allowance Sophie is paid as a function of the number of chores she completes in a month?
- It is a proportional function. (Incorrect. Sophie will be paid 15 dollars even if she doesn't complete any chores (if the function was proportional, she would be paid $0).)
- It is a linear, nonproportional function. (Correct. Sophie will be paid dollars if she completes chores in a month, and that is a linear function.)
- It is not a linear function. (Incorrect. Sophie will be paid dollars if she completes chores in a month, and that is a linear function.)
- There is not enough information to solve this problem. (Incorrect. How much would Sophie earn if she completed 0 chores? 1 chore? 2 chores? How about 5 chores? Is this a proportional or a linear relationship?)
A: It is a linear, nonproportional function.

Q: Jean's parents gave her a choice on how much allowance she will get in a month.

Choice 1: Jean gets an allowance of $15 each month plus an extra $2 for each chore she completes around the house.

Choice 2: Jean gets an allowance of $50 per month, but must complete 20 chores each month.

Which Choice should Jean make in order to earn the largest allowance if she plans to complete 20 chores each month?
- Both choices earn Jean the same allowance. (Incorrect. If Jean completes 20 chores each month, Choice 1 will earn her dollars. How much will Choice 2 earn her?)
- Choice 1 earns Jean a bigger allowance. (Correct. If Jean completes 20 chores each month, Choice 1 will earn her dollars, while Choice 2 will earn her $50.)
- Choice 2 earns Jean a bigger allowance. (Incorrect. If Jean completes 20 chores each month, Choice 1 will earn her dollars. How much will Choice 2 earn her?)
- There is not enough informaiton to determine which is a better Choice. (Incorrect. If Jean completes 20 chores each month, Choice 1 will earn her dollars. How much will Choice 2 earn her?)
A: Choice 1 earns Jean a bigger allowance.

Q: Sophie has been saving money at a regular rate and noticed that months after her 15th birthday, she had saved a total of dollars. Which of the following statements correctly describes her savings plan?
- By her 15th birthday, she had saved 20 dollars and was able to save an additional 224 dollars each month afterwards. (Incorrect. One month later, when , how much money did Sophie have? What does the +224 in the scenario refer to?)
- By her 15th birthday, she had saved 224 dollars and was able to save an additional 20 dollars each month afterwards. (Correct. On her 15th birthday, (0 months after her 15th birthday) she had dollars and 1 month later (when ) she had dollars, so she saved an additional 20 dollars that month.)
- She had saved a total of 244 dollars by her 16th birthday. (Incorrect. One month later, when , how much money did Sophie have? What does the +224 in the scenario refer to?)
- None of the above. (Incorrect. One month later, when , how much money did Sophie have? What does the +224 in the scenario refer to?)
A: By her 15th birthday, she had saved 224 dollars and was able to save an additional 20 dollars each month afterwards.

Q: A restaurant, famous for their eggrolls, has a pricing system that depends on the number of eggrolls that customers order. There is a "per customer fee" that everyone pays and a cost per eggroll that is added to the bill of those who order eggrolls.

Sophie determined that the function describing the cost of dinner is linear: if you order x eggrolls, your dinner will cost dollars. What is the "per eggroll fee"?
- $10.00 (Incorrect. Calculate the cost of purcashing 0 eggrolls ( ) and 1 eggroll ( ). The difference will be the per eggroll fee.)
- $1.50 (Correct. The per eggroll fee is the coefficient of in the function's equation, so the per eggroll fee is $1.50.)
- $11.50 (Incorrect. Calculate the cost of purcashing 0 eggrolls ( ) and 1 eggroll ( ). The difference will be the per eggroll fee.)
- None of the above. (Incorrect. Calculate the cost of purcashing 0 eggrolls ( ) and 1 eggroll ( ). The difference will be the per eggroll fee.)
A: $1.50

Q: Which statement best describes the function represented by the table below?

x | y
1 | 1
2 | -1
3 | 1
4 | -1
- It is a linear function. (Incorrect. Since the difference between consecutive outputs is not constant, this is not a linear function.)
- It is a nonlinear function. (Correct. The difference between consecutive outputs is not constant, so this is a nonlinear function.)
A: It is a nonlinear function.

Q: An inverse variation function has the property that when . What is the equation of the function?
A: (a choice with no text)
If wrong: Incorrect. It is true that when in this function, but this is a linear function, not an inverse variation function.
If wrong: Incorrect. It is true that when in this function, but this is a quadratic function, not an inverse variation function.
If wrong: Incorrect. It is true that when in this function, but this is a linear function, not an inverse variation function.
If right: Correct. This function has the correct form of an inverse variation function, , and when , .

Q: Which of the following statements is correct about the function graphed below?
- The function is undefined when . (Correct. The equation for this inverse function is . Since division by 0 is undefined, the function itself will be undefined when .)
- The graph of the function passes through the origin. (Incorrect. Look at the graph; the ordered pair (0, 0) does not lie on the graph of the function.)
- The ordered pair (3, 3) lies on the graph of the function. (Incorrect. Look at the graph; the ordered pair (3, 3) does not lie on the graph of the function.)
- The function is linear. (Incorrect. This graph is not a line, so it can not be a linear function.)
A: The function is undefined when .

Q: Does this graph represent a linear, quadratic, inverse variation, or exponential function?
- This is a linear function. (Incorrect. Check the curve of the graph. What does the shape tell you about the type of function that it is?)
- This is an inverse variation function. (Incorrect. Check the curve of the graph. What does the shape tell you about the type of function that it is?)
- This is an exponential function. (Incorrect. Check the curve of the graph. What does the shape tell you about the type of function that it is?)
- This is a quadratic function. (Correct. The graph is a parabola, so the function is quadratic.)
A: This is a quadratic function.

Q: The following partial table represents an exponential function. Which number belongs in the missing entry?

x | y
0 | 3
1 | 12
2 | 48
3 |
4 | 768
- 408 (Incorrect. Look at the pattern in the column of y-values: 12 is 4 times larger than 3, and 48 is 4 times larger than 12. Does this help you make a prediction?)
- 49 (Incorrect. Look at the pattern in the column of y-values: 12 is 4 times larger than 3, and 48 is 4 times larger than 12. Does this help you make a prediction?)
- 72 (Incorrect. Look at the pattern in the column of y-values: 12 is 4 times larger than 3, and 48 is 4 times larger than 12. Does this help you make a prediction?)
- 192 (Correct. Since the function is exponential, the quotient of consecutive outputs is constant. Here the quotient is 4, since , and . Multiplying .)
A: 192