Algebra 1 Chapter 3 Practice Test
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1 Algebra 1 Chapter 3 Practice Test 1. Which of the following represent functions? a. All b. I and II c. I and III d. II and III I. Input Output II. Input Output III. Input Output Determine whether the graph represents a function. a. The relation is not a function. b. The relation is a function. 3. Does the input-output table represent a function? If it does represent a function, list the domain and range. Input Output Which of the following data sets is best described by a linear function? a. c. b. d. 5. Classify the function as discrete or continuous for the given domain. Then identify the range of the function. ; domain 6. Classify the function as discrete or continuous for the given domain. Then identify the range of the function.
2 ; domain: x = 4, 2, 0, 2, 4 7. At a convenience store, bottles of water cost $1.20 each. The function gives the cost of buying x bottles. Give a reasonable domain and range for the function in this context. 8. Evaluate, when x = 2. a. 18 c. 3 b. 33 d For, what is the value of x for which? a. c. b. d. 10. The domain of the function f is the set of integers greater than. Which of the following values represent elements of the range of? a. e. b. f. c. g. d. h. 11. For the function f, each range value is associated with only one domain value. The range of is. What is the domain of? Explain your answer. 12. Use intercepts to graph the linear equation. a. x-intercept: , y-intercept: 3 c. x-intercept: 9, y-intercept: 22 3 y y x x b. x-intercept: 15 2, y-intercept: 6 d. x-intercept: 9, y-intercept: 6
3 y y x x Graph the function. a. c. b. d. 14. The Tome family is renting a car for a few days. Meinke Rentals charges $48 per day, plus a fixed cleaning fee of $30. The function represents the cost to rent a car from Meinke Rentals for d days. SmartRent charges $60 per day. The function represents the cost to rent a car from SmartRent for d days. Graph M and S on the same coordinate plane. Describe the transformations from the graph of M to the graph of S..
4 a. c. b. A vertical shift down 30 units, followed by a vertical stretch by a factor of d. A vertical shrink by a factor of 0.8, followed by a vertical shift up 24 units. A vertical stretch by a factor of 1.25, followed by a vertical shift down 30 units. A vertical shift up 24 units, followed by a vertical shrink by a factor of The pressure in a car tire is given by where p is pressure in psi and x is the number of months since the tire was filled. Describe what this function represents. a. The initial tire pressure is 30 psi, and it goes down by 1 psi each month. b. The initial tire pressure is 30 psi, and it increases by 1 psi each month. c. The initial tire pressure is 1 psi, and it increases by 30 psi each month. d. The initial tire pressure is 1 psi, and it goes down by 30 psi each month. 16. The graph shows membership costs at a gym. What is the cost per month?
5 17. Describe the effect of the transformation. a. vertical translation of 9 units c. vertical stretch with reflection b. horizontal translation of 9 units d. vertical stretch without reflection 18. Let be a vertical shift of down 8 units followed by a vertical shrink by a factor of. Write the rule for. a. c. b. d. 19. What must be done to the graph of to obtain the graph of the function? a. b. c. d. The graph of f is shifted left 6 units, horizontally shrunk by a factor of, and shifted down 8 units. The graph of f is shifted right 6 units, vertically shrunk by a factor of, and shifted down 8 units. The graph of f is shifted left 6 units, vertically shrunk by a factor of, and shifted down 8 units. The graph of f is shifted left 6 units, vertically shrunk by a factor of, and shifted up 8 units. 20. What is the vertex of the graph?
6 a. c. b. d.
7 Algebra 1 Chapter 3 Practice Test Answer Section 1. ANS: B PTS: 1 REF: A1.01.EN.ST.10 NAT: NT.CCSS.MTH F.IF.1 LOC: NCTM.PSSM.00.MTH.9-12.ALG.1.b KEY: functions DOK: DOK 1 NOT: Sec ANS: B PTS: 1 REF: 0821e390-1a76-11df-b9de-001e33aa91d2 NAT: NT.CCSS.MTH F.IF.1 LOC: NCTM.PSSM.00.MTH.9-12.ALG.1.b KEY: functions relations vertical line test DOK: DOK 1 NOT: Sec ANS: Yes, the table does represent a function. The collection of the input values is the domain: 1, 2, 3, and 4; the collection of output values is the range: 7, 11, 15, and 19. PTS: 1 REF: MALG0194 NAT: NT.CCSS.MTH F.IF.1 LOC: NCTM.PSSM.00.MTH.9-12.ALG.4.a TOP: Represent Functions as Rules and Tables KEY: equation function table DOK: DOK 1 NOT: Sec ANS: C PTS: 1 NAT: NT.CCSS.MTH F.LE.1 DOK: DOK 1 NOT: Sec ANS: The function is continuous. The range is. PTS: 1 REF: 08f5bdf0-1a76-11df-b9de-001e33aa91d2 NAT: NT.CCSS.MTH F.IF.5 LOC: NCTM.PSSM.00.MTH.9-12.ALG.1.c TOP: Identify Discrete and Continuous Functions KEY: discrete continuous DOK: DOK 1 NOT: Sec ANS: The function is discrete. The range is 3, 4, 5, 6, and 7 PTS: 1 REF: 0901a4d0-1a76-11df-b9de-001e33aa91d2 NAT: NT.CCSS.MTH F.IF.5 LOC: NCTM.PSSM.00.MTH.9-12.ALG.1.c TOP: Identify Discrete and Continuous Functions KEY: discrete continuous DOK: DOK 1 NOT: Sec ANS: domain: ; range: PTS: 1 NAT: NT.CCSS.MTH F.IF.5 DOK: DOK 1 NOT: Sec ANS: D PTS: 1 REF: 1068edc df-9c7d f0d2ea OBJ: Evaluating Functions NAT: NT.CCSS.MTH F.IF.1 NT.CCSS.MTH F.IF.2 STA: PA.PAAS.MTH R LOC: MTH.C TOP: Writing Functions KEY: function input output evaluate DOK: DOK 2 NOT: Sec ANS: C PTS: 1 NAT: NT.CCSS.MTH F.IF.2 DOK: DOK 2 NOT: Sec ANS: B, D, F, G
8 A: 2.5 is not an integer, so it is not in the domain of. does not represent an element of the range of. B: is an integer and it is greater than, so it is in the domain of. is the element of the range assigned to. C: is an integer, but it is not greater than, so it is not in the domain of. does not represent an element of the range of. D: 4 is an integer and it is greater than, so it is in the domain of. is the element of the range assigned to 4. E: is not an integer, so it is not in the domain of. does not represent an element of the range of. F: 0 is an integer and it is greater than, so it is in the domain of. is the element of the range assigned to 0. G: 8 is an integer and it is greater than, so it is in the domain of. is the element of the range assigned to 8. H: is an integer, but it is not greater than, so it is not in the domain of. does not represent an element of the range of. Correct Incorrect Feedback That s correct! A function assigns each element of its domain to exactly one element of its range. PTS: 2 NAT: NT.CCSS.MTH F.IF.1 KEY: function domain range function values DOK: DOK 1 NOT: Sec ANS: The domain of is. Since the range is value, the domain must contain only the values of, and each range value is associated with only one domain being mapped to each of the range values. So, the domain contains, 7, 9.7, 14, and 21. Rubric 1 point for the domain; 2 points for explanation PTS: 3 NAT: NT.CCSS.MTH F.IF.1 NT.CCSS.MTH.10.K-12.MP.3 KEY: function domain range DOK: DOK 2 NOT: Sec ANS: D PTS: 1 REF: 10b df-9c7d f0d2ea OBJ: Graphing Linear Equations by Using Intercepts NAT: NT.CCSS.MTH F.IF.7.a STA: PA.PAAS.MTH K PA.PAAA.MTH M11.D LOC: MTH.C TOP: Using Intercepts
9 KEY: linear equation graphing x-intercept y-intercept intercepts DOK: DOK 1 NOT: Sec ANS: C PTS: 1 REF: 106db27a df-9c7d f0d2ea OBJ: Graphing Functions NAT: NT.CCSS.MTH A.REI.10 NT.CCSS.MTH F.IF.2 STA: PA.PAAS.MTH Q PA.PAAS.MTH R PA.PAAA.MTH M11.D PA.PAAA.MTH M11.D LOC: MTH.C TOP: Graphing Functions KEY: graph function DOK: DOK 2 NOT: Sec ANS: A PTS: 1 REF: df-9c7d f0d2ea OBJ: Application NAT: NT.CCSS.MTH A.CED.2 NT.CCSS.MTH F.BF.3 TOP: Transforming Linear Functions KEY: transform linear functions DOK: DOK 2 NOT: Sec 3.5 and ANS: A PTS: 1 NAT: NT.CCSS.MTH F.LE.5 KEY: linear function parameter DOK: DOK 1 NOT: Sec ANS: $25 PTS: 1 NAT: NT.CCSS.MTH F.IF.4 DOK: DOK 1 NOT: Sec ANS: D PTS: 1 REF: 08e9d710-1a76-11df-b9de-001e33aa91d2 NAT: NT.CCSS.MTH F.BF.3 DOK: DOK 2 NOT: Sec ANS: C PTS: 1 REF: 14784b df-9c7d f0d2ea OBJ: Combining Transformations of Linear Functions NAT: NT.CCSS.MTH A.CED.2 NT.CCSS.MTH F.BF.3 LOC: MTH.C TOP: Transforming Linear Functions KEY: transform linear functions shift translate stretch DOK: DOK 2 NOT: Sec ANS: C Follow the order of operations to apply the transformations. First, notice that 6 is being added to inside the absolute value bars. So, the graph of f is shifted left 6 units. Now, notice that the absolute value expression is being multiplied by. So, the graph of f is being vertically shrunk by a factor of. Finally, 8 is being subtracted from the first term of f. So, the graph of f is being shifted down 8 units. Feedback A Recall that a horizontal shrink occurs when is multiplied by a constant, where, before any horizontal shifts occur. B In horizontal shifts of the form, where is a constant, the graph is moved in the opposite direction of the sign of. C That s correct! D In vertical shifts of the form, where is a constant, the graph is moved in the same direction of the sign of. PTS: 1 NAT: NT.CCSS.MTH F.BF.3 KEY: absolute value function vertical stretch horizontal shifts vertical shifts transformations DOK: DOK 1 NOT: Sec ANS: C
10 The vertex is. A B C D Feedback This is one of the points where the function intersects the x-axis. This is the point where the function intersects the y-axis. That s correct! This is one of the points where the function intersects the x-axis. PTS: 1 NAT: NT.CCSS.MTH F.IF.7.b* KEY: absolute value function graph of a function function vertex DOK: DOK 1 NOT: Sec 3.7
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