2.4-2.7_Quiz_A

© 2023 Jean Adams Flamingo Math.com Unit 2 2.4 – 2.7 Quiz Form A 1. The function 𝑓𝑓 is given by 𝑓𝑓 𝑥𝑥 = 𝑥𝑥 2 − 4 and the function 𝑔𝑔 is given by 𝑔𝑔 𝑥𝑥 = 𝑥𝑥+3 𝑥𝑥 . Find an expression for 𝑓𝑓 𝑔𝑔 𝑥𝑥 A. 𝑥𝑥 2 + 6𝑥𝑥 + 5 𝑥𝑥 2 B. 𝑥𝑥 2 + 𝑥𝑥 − 1 𝑥𝑥 2 C. − 3 𝑥𝑥 2 − 2𝑥𝑥 − 3 𝑥𝑥 2 D. 𝑥𝑥 2 + 5 𝑥𝑥 2 2. The table gives values for the functions 𝑓𝑓 and 𝑔𝑔 at selected values of 𝑥𝑥 . Functions 𝑓𝑓 and 𝑔𝑔 are defined for all real numbers. Let ℎ be the function defined by ℎ 𝑥𝑥 = 𝑓𝑓 𝑔𝑔 𝑥𝑥 . What is the value of ℎ (0) ? A. − 4 B. − 3 C. 1 D. 3 𝒙𝒙 − 2 − 1 0 1 2 𝒇𝒇 ( 𝒙𝒙 ) 5 3 0 − 2 − 4 𝒈𝒈 ( 𝒙𝒙 ) − 3 0 2 − 1 1 3. The function 𝑔𝑔 is given by 𝑔𝑔 𝑥𝑥 = 4 � 49 𝑥𝑥 . Which of the following is an equivalent form for 𝑔𝑔 ( 𝑥𝑥 ) ? A. 𝑔𝑔 𝑥𝑥 = 2 � 7 ( 𝑥𝑥 / 2 ) B. 𝑔𝑔 𝑥𝑥 = 2 � 7 ( 2𝑥𝑥 ) C. 𝑔𝑔 𝑥𝑥 = 4 � 7 ( 𝑥𝑥 / 2 ) D. 𝑔𝑔 𝑥𝑥 = 4 � 7 ( 2𝑥𝑥 )

© 2023 Jean Adams Flamingo Math.com 5. The increasing function 𝑃𝑃 gives the number of followers, in thousands, for an influencer on a social media platform. The table gives the values of 𝑃𝑃 ( 𝑡𝑡 ) for selected values of 𝑡𝑡 , in weeks, since the influencer created their account on the social media site. Which of the following models would best represent these data for the scenario? A. 𝑦𝑦 = 9𝑡𝑡 + 18 B. 𝑦𝑦 = 235 16 𝑡𝑡 + 18 C. 𝑦𝑦 = 18 3 2 𝑡𝑡 D. 𝑦𝑦 = 18 2 3 𝑡𝑡 𝒕𝒕 (weeks) 0 1 2 3 4 𝑷𝑷 ( 𝒕𝒕 ) (thousands) 18 27 40.5 60.75 91.125 4. The functions 𝑓𝑓 and 𝑔𝑔 are defined for all real numbers such that 𝑔𝑔 𝑥𝑥 = 𝑓𝑓 3 𝑥𝑥 − 2 . Which of the following sequences of transformations maps the graph of 𝑓𝑓 to the graph of 𝑔𝑔 in the 𝑥𝑥𝑦𝑦 − plane? A. Horizontal dilation of the graph of 𝑓𝑓 by a factor of 1 3 , followed by a horizontal translation of 𝑓𝑓 by 2 units to the right. B. Horizontal dilation of the graph of 𝑓𝑓 by a factor of 1 3 , followed by a horizontal translation of 𝑓𝑓 by 2 units to the left. C. Horizontal dilation of the graph of 𝑓𝑓 by a factor of 3 , followed by a horizontal translation of 𝑓𝑓 by 2 units to the right. D. Horizontal dilation of the graph of 𝑓𝑓 by a factor of 3 , followed by a horizontal translation of 𝑓𝑓 by 2 units to the left.

© 2023 Jean Adams Flamingo Math.com 9. The sales department of a manufacturing company is estimating projected sales data for a new product under development. A linear regression was used to develop a model for the sales over time. The figure above shows a graph of the residuals of the linear regression. Which of the following statements about the linear regression is true? A. The linear model is not appropriate , because there is a clear pattern in the graph of the residuals. B. The linear model is not appropriate , because the graph of the residuals have more points above zero than below zero. C. The linear model is appropriate , because there is a clear pattern in the graph of the residuals. D. The linear model is appropriate , because the positive residuals and the negative residuals are balanced equally. 10. The table gives values of the function 𝑔𝑔 for selected values of 𝑥𝑥 . The function 𝑓𝑓 is given by 𝑓𝑓 𝑥𝑥 = 2 𝑥𝑥 + 𝑥𝑥 2 . What is the value of 𝑓𝑓 𝑔𝑔 2 ? A. 100 B. 73 8 C. 15 D. 17 − 12 12 Time Residuals 0 𝒙𝒙 − 3 0 2 4 8 𝒈𝒈 ( 𝒙𝒙 ) 6 2 − 3 7 15

The Asian lady beetle is an invasive species that look similar to the ladybug, at first sight. These beetles can become a problem for homeowners and gardeners. They can overtake the native ladybug population. You have called an insect specialist to help you keep the good ladybugs and spray insecticide on the beetle species that is ruining your garden. The population for each insect is given by the equations below, 𝐿𝐿 ( 𝑡𝑡 ) is the population of ladybugs, where t is in days. 𝐵𝐵 ( 𝑡𝑡 ) is the population of the Asian beetle, t days after being sprayed. A. What is the initial population of each species when the specialist arrives at 𝑡𝑡 = 0 ? B. How many days will it take for the ladybug species to reach a population of 5000 ladybugs ? C. How long will it take for the Asian beetle species to be cut in half after the beetle population has been sprayed? D. Will the two species ever have the same number of insects? If so, when will this happen? What is the population, at this time? Explain how you arrived at your answer. © 2023 Jean Adams Flamingo Math.com Unit 2 2.4 – 2.7 Quiz Form A Calculator ACTIVE Ladybug species Asian beetle species 𝐿𝐿 𝑡𝑡 = 2000 𝑒𝑒 0 . 025𝑡𝑡 𝐵𝐵 𝑡𝑡 = 3600 2 3 0 . 075𝑡𝑡

© 2023 Jean Adams Flamingo Math.com Name ________________________________________________________ Date _________________________ Period __________ QUIZ 2.4-2.7 Free Response Question Part A. Part B. Part C. Part D.