Chapter 1 Review Answer Key

Question 1 __/9 a. b. d. c. e. +1 +1 graph +1 +1 table +1 labels +1 Create a table and graph from the following situation. You are buying some new pens on Amazon. You see that each pen is going to cost you $2. When you order (even if you don’t order any pens) there is a flat $5 shipping fee. What is the equation that models this situation? 𝑦=2𝑥+5 -or- 𝐶=2𝑛+5 +1 # of Pens Cost in $ 5 1 7 2 9 3 11 4 13 15 Cost +1 graph Find an equation for the inverse. 𝑛= 𝐶−5 2 -or- 𝑦= 𝑥−5 2 +1 # of Pens +1 table +1 labels Create a table and graph of the inverse of the situation. How can we tell if two tables are inverses of each other? Cost in $ # of Pens 5 7 1 9 2 11 3 13 4 15 # of Pens The domain and range are flipped. -or- The x-variable and y-variable are flipped. The independent and dependent variable are flipped. The output and input are flipped. +1 +1 graph +1 labels +1 table Cost

Question 2 __/10 They are reflections across the y=x line. a. c. d. b. Create a table and graph from the following situation. You throw a ball off a cliff and measure how long it takes to fall and come up with the following model: 𝑑=−2 𝑡 2 +50 where d is the distance from the ground in feet and t is time measured in seconds. Find the inverse equation. 𝑡= 𝑑−50 −2 -or- 𝑦= 𝑥−50 −2 +1 Time (sec) Distance (feet) 50 1 48 2 42 3 32 4 18 5 +1 graph Distance How many seconds would it take the ball to fall 20 feet? +1 labels +1 table +1 𝑡≈3.87𝑠𝑒𝑐 Time Create a table and graph of the inverse of the situation. How can we tell if two graphs are inverses of each other? Distance (feet) Time (sec) 50 48 1 42 2 32 3 18 4 5 Time +1 labels +1 graph They are reflections across the y=x line. +1 +1 labels +1 table Distance

Question 3 __/10 𝑧= 2 8 +1 𝑧=256+1 𝑧=257 𝑧𝑒𝑏𝑟𝑎𝑠 2 𝑡 +1=3,000 a. b. c. d. Create a table and graph from the following situation. You are a biologist studying zebras in Africa. You discover that the rate of growth of zebras can be modeled by 𝑧= 2 𝑡 +1 where z is the number of zebras and t is the time in years. How many zebras will there be after 8 years? +1 𝑧= 2 8 +1 𝑧=256+1 𝑧=257 𝑧𝑒𝑏𝑟𝑎𝑠 Time (years) # of Zebras 2 1 3 5 9 4 17 33 +1 labels # of Zebras +1 graph +1 labels +1 table Time Create a table and graph of the inverse of the situation. About how many years will it take to get 3,000 zebras? # of Zebras Time (years) 2 3 1 5 9 17 4 33 Time 2 𝑡 +1=3,000 2 11 +1=2,049 2 11.5 +1=2,897 2 11.55 +1=2,999 About 11.55 years +1 +1 labels +1 graph +1 labels +1 table # of Zebras

Question 4 Question 5 __/3 __/3 What are 3 other words that we use to describe the x-variable? Domain Input Independent Variable +1 +1 +1 Question 5 __/3 What are 3 other words that we use to describe the y-variable? Range Output Dedependent Variable +1 +1 +1

Question 6 Question 7 Question 8 __/2 __/2 __/1 If 𝑓 8 =15 what is 𝑓 −1 15 ? How do you know? 𝑓 −1 15 =8 Something about inverses and flipping input and output +1 +1 Question 7 __/2 If 𝑓 2 3 =3.14 what is 𝑓 −1 3.14 ? How do you know? 𝑓 −1 3.14 = 2 3 Something about inverses and flipping input and output +1 +1 Question 8 __/1 If 𝑓 𝑠 =𝑡 what is 𝑓 −1 𝑡 ? 𝑓 −1 𝑡 =𝑠 +1

Question 9 __/12 Steps to undo: 1) Add 6 Steps to undo: Take the following functions and find their inverse function. Describe how you would undo the function in words and then write out the inverse equation. a. b. c. d. e. f. 𝑓 𝑥 =𝑥−6 𝑓 𝑥 = 𝑥 12 𝑓 𝑥 =4𝑥+7 Steps to undo: 1) Add 6 Steps to undo: 1) Multiply by 12 Steps to undo: Subtract 7 Divide by 4 +1 +1 +1 𝑓 −1 𝑥 =𝑥+6 +1 𝑓 −1 𝑥 =12𝑥 +1 𝑓 −1 𝑥 = 𝑥−7 4 +1 𝑓 𝑥 = 𝑥 2 −9 𝑓 𝑥 = 2 𝑥 𝑓 𝑥 = 2 𝑥 +4 Steps to undo: Add 9 Take the square root Steps to undo: Subtract 4 Take the log of base 2 Steps to undo: Take the log of base 2 +1 +1 +1 +1 +1 𝑓 −1 𝑥 = 𝑥+9 𝑓 −1 𝑥 = log 2 𝑥 +1 𝑓 −1 𝑥 = log 2 (𝑥−4)

Question 10 __/4 Change the exponential form of the equation into the logarithmic form. a. b. c. d. 2 3 =8 3 4 =81 log 2 8 =3 log 3 81 =4 +1 +1 10 2 =100 2 −1 = 1 2 log 10 100 =2 log 2 1 2 =−1 +1 +1

Total __/56 Once you have totaled your partners score, give the review back to them. Once you have your own review back, come to me and tell me what your score was.