Name: _____________________________________ Chapter #4: Functions Period: _____________ Date: ______________ Homework Packet #8 Days 1 – 5 COMPLETE THE FOLLOWING IN PENCIL ONLY. After completing the assignment, use the answer key and a COLORED PEN to correct your work. Use your notes to help you answer the following. Answers are provided. #1 Intro to Functions In each of the following examples, use an input-output chart to decide if the following relation is a function. If your answer is NO, explain why. 1. Consider the following relation: multiply the input by five and then subtract seven to get the output. 2. Consider the following table; 3. Consider the following graph 4. Consider the following graph 1 For questions #5-9 use the graph below. Charlene heads out to school by foot on a fine spring day. Her distance from school, in blocks, is given as a function of the time, in minutes, she has been walking. This function is represented by the graph below. 5. How far does Charlene start off from school? 6. What is her distance from school after she has been walking for 4 minutes? 7. After walking for six minutes, Charlene stops to look for her subway pass. How long does she stop for? 8. Charlene then walks to a subway station before heading to school on the subway. How many blocks did she walk to the subway? 9. How long did it take for her to get to school once she got on the train? 2 #2 Function Review Activity Determine whether each relation is a function. Explain. 1. 2. 3. 4. 5. 6. 7. {(6, -1), (-4, 2), (5, 2), (4, 6), (6, 5)} 8. 9. {(2, 5), (4, -2), (3, 3), (5, 4), (-2, 5)} 10. 𝑥 = −3 11. 𝑦 = 𝑥 2 − 2 3 MIXED REVIEW: Andrew has a new job at the local pizza store as a delivery boy. The following graph shows one of his deliveries he made. Analyze the graph and answer questions #12-15. 12. How long was the entire trip? 13. If he arrived at the house after 4 minutes, how far away was the house from the pizza place? 14. Why might Andrew have stopped 3 times for 1 minute? 15. Was Andrew’s trip longer going to the house or coming back? 16. Determine whether each number is a solution of √ 𝑥 + 2 ≥ 2. a) 2 b) -1 17. Determine whether each number is a solution of 𝑥 2 + 3𝑥 = 18. a) 3 b) -3 4 #3 Function Notation, Day 1 Questions #1-4: Given the function f defined by the formula f (x) = 2x + 1, find the following: 1. f (4) 2. f (-5) 1 4. 𝑓 (2) 3. f (0) 𝑥 5. MULTIPLE CHOICE: If the function f (x) is defined by f(x) = 2 − 6, then which of the following is the value of f (10)? Show all of your work! a. -1 b. 2 c. 14 d. 7 3 6. MULTIPLE CHOICE: If the function f (x) = 2x – 3 and g (x) = 2 𝑥 + 1 then which of the following is a true statement? Show all of your work! a. 𝑓(0) > 𝑔(0) b. 𝑓(2) = 𝑔(2) c. 𝑓(8) = 𝑔(8) d. 𝑔(4) < 𝑓(4) 5 MIXED REVIEW: 7. Consider the function f (x) = 3(2 - x) – 2. Fill out the function table below for the inputs given and graph the function on the axes provided. Make sure you label your function. Determine whether each relation is a function. Explain. 8. 9. Solve each equation for y. 10. y + 4x = 8 11. 2y = 8x 12. 3y + 6x = 12 6 #4 Function Notation, Day 2 Questions #1-5: If 𝒇(𝒙) = 𝒙𝟐 + 𝟓𝒙 − 𝟐𝟒 𝒂𝒏𝒅 𝒈(𝒙) = 𝒙𝟐 − 𝟒. 1. Find f (-3) 2. Find f (m) 4. g (a) + 9 5. f (2) + g (-2) 3. Find g (5) Questions #6-10: If 𝒇(𝒙) = −𝟐𝒙 − 𝟑 𝒂𝒏𝒅 𝒈(𝒙) = 𝒙𝟐 + 𝟓𝒙. 6. Find g (-3) 9. g (a) + 9 7. Find 5[f (d)] 8. Find g (-6m) 10. f (2) + g (-2) 7 MIXED REVIEW: Questions #11-14: Given the function g defined by the formula g (x) = 11. g (9) 12. g (0) 13. g (3) 14. g (17) 𝑥−5 2 , find the following: Questions #15-18: Given the function f defined by the formula f (x) = 𝑥 2 − 4, find the following: 15. f (3) 1 17. 𝑓 (4) 16. f (-4) 18. f (-2) 8 #5 Illustrating Function Notation with a table/graph 1. Jenna knits scarves and then sells them on Etsy, an online marketplace. Let C(x) = 4x + 20 represent the cost C in dollars to produce from 1 to 6 scarves. Fill in the table to show the relationship between the number of scarves x and the cost C. x, Number of Scarves Show work here C(x), Cost in dollars 4. If the pattern continues, find the number of scarves such that C(x) = 80. 2. For what value of x is C(x) = 28? 3. For what value of x is C(x) = 40? 5. From the table below list two possible solutions to the equation f(x) = 0. Use the function shown in the table to answer the following. x 1 2 3 4 f(x) 1 4 9 16 8. If f(x) = 4, then x = _________ 6. f (3) = _________ 7. f (4) = __________ 9. If f(x) = 16, then x = ___________ 9 Based on the graph of the function 𝑦 = 𝑔(𝑥) shown below, answer the following questions. Evaluate each of the following and illustrate with a point on the graph. 10. 𝑔(−2) = ________ 11. 𝑔(0) = _________ 12. 𝑔(3) = _________ 13. 𝑔(7) = _________ 14. What value of x solves the equation 𝑔(𝑥) = 0 . These are called the zeroes of the function. 15. How many values of x solve the equation 𝑔(𝑥) = 2? How can you illustrate your answer on the graph? Remember, we are not looking for exact x-values, only how many solutions. MIXED REVIEW: 16. If f(x) = x2 – 3x + 8, evaluate f(-3). −𝒃+√𝒃𝟐 −𝟒𝒂𝒄 17. Evaluate 𝟐𝒂 to the nearest tenth. when a = 2, b = -8, c = -1 18. Solve, graph, write the solution set in interval notation: |2x – 3| < 5 10 Homework Packet #8 Answers: #5 Illustrating Function Notation #1 Intro to Functions #3 Function Notation Day 1 1. -22, -7, 23; yes 1. 9 2. no 2. -9 3. 3, 1, 4; yes 3. 1 2. 2 4. 1, 2, 3, 4, and 8; no 4. 2 3. 5 5. 22 blocks 5. A 4. 15 6. 14 blocks 6. C 7. 3 minutes 7. (-2, 10), (-1, 7), (0, 4), 8. 2 blocks 9. 4 minutes (1, 1), (2, -2); correct graph 8. yes, provide explanation 1. See table at bottom of page 5. 𝑥 = √2 or 𝑥 = 𝜋 6. 9 7. 16 9. no, provide explanation 8. 2 10. y = -4x + 8 9. 4 1. yes, provide explanation 11. y = 4x 10. -3, put dot on graph 2. no, provide explanation 12. y = -2x + 4 11. -3, put dot on graph #2 Function Review Activity 3. yes, provide explanation 4. no, provide explanation 5. no, provide explanation 6. yes, provide explanation 7. no, provide explanation 8. no, provide explanation 9. yes, provide explanation 10. no, provide explanation 11. yes, provide explanation 12. 15 minutes 13. 9 blocks 14. red lights 15. coming back 16. a) yes b) no 17. a) yes b) no 12. 4, put dot on graph #4 Function Notation Day 2 1. -30 2. 𝑚2 + 5𝑚 − 24 3. 21 4. a2 + 5 5. -10 6. -6 7. -10d – 15 8. 36m2 – 30m 9. a2 + 5a + 9 10. -13 11. 2 12. -2.5 13. -1 14. 6 15. 5 16. 12 63 17. − 16 or -3.9375 18. 0 13. 0, put dot on graph 14. x = -3, 1, 5, and 7 15. 4, explain how you can illustrate it on the graph. 16. 26 17. 4.1 18. correct graph; (-1, 4) 11 12