Review: 2.1 through 2.8 Show work for credit. Find the equation that gives the with term of each sequence. (2.1) 5 5 1) 10,5,7 7. 2) - 5,-9,-13, -17, . WIN 4) Which of the following could represent the equation of the sequence {10, 2, -6, -14, ...}? Select all that apply. (2.1) I. f(n) = 10 - 8(n - 1) II. f(n) = -8 + 10n III. f(n) = -8 + 10(n - 1) IV. f(n) = 18 - 8n V. f(n) = 10 - 8n VL f(n) = 2 -8(n + 2) 5) Which of the following could represent the equation of the sequence {; 2, 8, 32, ...}? (2.1) II. /() =(4)"-1 III. f(n) = 8(4)+3 TV. f(n) = 2 ()" 17-2 V. f(n) =!(4)* 6) The first term in the arithmetic sequence is 4, and the common difference is 3. What is the seventh term? (2.1) (A) 22 (B) 25 (C) 972 (D) 2,916State whether the following represent linear or exponential function. Explain. (2.2) 7) X 1 5 9 -4 -2 0 (x) 2 6 18 f(x) 5 1 -3 9 ) The third term of a sequence is 5, and the fifth term of the sequence is 20. Of the following, which statement is true? (A) If the sequence is arithmetic. the first term could be -25? ( 2.2) (B) If the sequence is arithmetic, the fourth term could be 7.5? (C) If the sequence is geometric, the fourth term could be 7? (D) If the sequence is geometric, the sixth term could be 40? 10) f(x) = 6 ()", then find: (2.3) 11) f(x) = -(0.4)*, then find: (2.3) a. Is the function increasing or decreasing? a. Is the function increasing or decreasing? b. Is the function concave up or concave down? b. Is the function concave up or concave down? c. Find lim f(x) = X-00 c. Find lim / (x) = d. Find lim f(x) = x-+00 d. Find lim f(x) = X+00 Note: You may need to look at your notes for the appropriate graph from 2.3.12) (2.3) 2 40 20 10 5 The exponential function f is defined by f (x) = abt, where a and b are positive constants. The table gives values of f (x) at selected values of x. Which of the following statements is true? (A) f demonstrates exponential decay because a > 0 and 0 0 and b > 1. (C) f demonstrates exponential growth because a > 0 and 0 0 and b > 1. Name the transformation in each function f. (2.4) 13) f (x) = 3* and g(x) = f(x) . 27 14) f (x) = 5* and g(x) = ((f(x))-2 15) f(x) = 7* and g(x) = _f(x) 49Evaluate each function at the given input value. (2.4) 16) Let h(x) = 2 . 37. Find h(1). 18) Let h(x) = 2 . 65. Find h(-1). 19) Before Facebook, we (old people) had MySpace, the first social networking site that reached a global audience. At its peak in 2008, MySpace was averaging over 100 million daily visitors. However, as Facebook rose in popularity, MySpace became less and less popular. The table shows the number of daily visitors to MySpace (in millions) m months since January 2009. (2.5) (months since Jan. 2009) 6 15 18 24 30 39 Vim) 25 20.5 13.5 10 5.5 2.6 1.7 (daily visitors in millions) a) Use the data in the table to create an exponential regression model of the form y = ab, where y represents the number of daily visitors to Myspace (in millions) x months since January 2009. b) Based on the model found in part a. when did the number of daily visitors to MySpace first drop below one million visitors?20) The table below shows the number of products sold (in thousands) for a company for several years since 2008. Fill in the last two columns as needed to answer questions a through d. (2.6) t (years) PO projected product sold residual 3 42.4 6 51.5 7 58.6 10 73.2 12 83.7 14 92.4 a) Find the projected exponential regression model using a graphing calculator. b) Plot the residual below using the appropriate scale. c) Based on the plot, is there a pattern? Is the predicted line the best for the data? Explain. d) Does the projected model overestimate or underestimate the number of products sold in the year 2013? Explain. If f(x) = 4x - 2 and g(x) = 2x2 - 7, then find: (2.7) 21) Find (f - g)(x) 22) Find (f = g) (x) 23) Find (g . f) (2)-1 1 4 6 11 f(x) 4 6 11 16 (2.7) The table gives the values of the function g for selected values of x. The function f is given by g (x) = 2* - x3. Find each of the following: 24) 9(f(-1)) 25) f(9 (3)) Find the inverse of each function. (2.8) 26) f (x) = 3 x- 1 27) f (x) = vx - 9: forx50