2.1 through 2.8 (10-27-23) 1 2 3 4 5 6 7 8 9 10 11 12) 13) 14) 15) 16 17) 18) 19 20 21 22 23 Question 1 L g(x) -2 4 0 3 -2 4 3 36 9 The table gives values of the function g for selected values of x. The function f is given by f(x) = 3 + x2. What is the value of f(g(3)) ? A -72 B C D 97Question 2 -2. -3- Graph of f The piecewise-linear function f, defined on -4 /2). What is the value of h (1) ? A) -5v3 DQuestion 5 -2 -1 1 2 f(I) 1 2 -1 -2 0 g(I) 2 0 1 -1 0 The table gives values for the functions f and g at selected values of I. Functions f and g are defined for all real numbers. Let h be the function defined by h(I) = f(g()). What is the value of h(0) ? A -2 B -1 C 0 D 22 3 4 5 6 7 8 9 10 1 13 14 15 16 17 18 19 20 21 22 23 2.5 1.5- 0.5. 0 -0.5 -1- -1.5- -2- -2.5- -3- -3.5- -4.5 Exponential Residual Plot -3 The graphs give three residual plots for linear, quadratic, and exponential regressions. Which of the following is true about the residual plots for these regressions? A The residual plots for the linear and exponential regressions are without pattern, and the residual plot for the quadratic regression shows a pattern. Therefore, the quadratic model is appropriate. The residual plot for the quadratic regression is without pattern, and the residual plots for the linear and exponential regressions show patterns. Therefore, the linear and exponential models are appropriate. C The residual plots for the linear and exponential regressions are without pattern, and the residual plot for the quadratic regression shows a pattern. Therefore, the linear and exponential models are appropriate. D The residual plot for the quadratic regression is without pattern, and the residual plots for the linear and exponential regressions show patterns. Therefore, the quadratic model is appropriate.Question 8 Residuals O The students in a precalculus class measured each student's height and arm span, in centimeters. The students calculated a linear regression y = a + br with heights as the input values and arm spans as the output values. The given residual plot has a point labeled P at coordinates (175,23.4). What does point P indicate in the context? A Because point P is above the I-axis, for the student with a height of 175 cm, the model overestimates the actual arm span value by 23.4 cm. B Because point Pis above the r-axis, for the student with a height of 175 cm, the model underestimates the actual arm span value by 23.4 cm. C Because point Pis above the I-axis, for the student with an arm span of 175 cm, the model overestimates the actual height value by 23.4 cm. D Because point Pis above the r-axis, for the student with an arm span of 175 cm, the model underestimates the actual height value by 23.4 cm.Question 9 The fifth term of a geometric sequence is 24, and the sixth term is 48. What is the value of the tenth term? A 144 B 168 C 768 (D 1536Question 10 t (months) 1 2 3 P(t) (thousands) 20 30 45 67.5 101.25 The increasing function P gives the number of followers, in thousands, for a new musical group on a social media site. The table gives values of P(t) for selected values of t, in months, since the musical group created their account on this social media site. If a model is constructed to represent these data, which of the following best applies to this situation? A y = 10t + 20 B y= 16 + 20 C y = 20(3)' D y = 20 (2)'Question 11 An exponential function G has a known common ratio of = and includes the input-output pair (1,4). Which of the following could define G(I) ? A 4+-(2-1) B .4" D 4 . (4 )(3-1)Question 12 Day 5 Amount 2 6.315 (grams) The table gives values for the amount of a certain substance, in grams, on certain days. The data are modeled by an exponential function f given by f(t) = 2e(), where t is the number of days since day 0. The constant r is defined as the continuous growth rate of this model. Based on the table, what is the value of r ? A 0.230 B 0.259 C 0.863 D 1.259Question 13 The functions f and g are given by f(I) = 2" and g(I) = 2" . 2", where a > 0. Which of the following describes the relationship between the graph of f and the graph of g? A The graph of g is a vertical translation of the graph of f by a units. B The graph of g is a horizontal translation of the graph of f by a units. C The graph of g is a vertical translation of the graph of f by -a units. D The graph of g is a horizontal translation of the graph of f by -a units.E Question 14 For an arithmetic sequence S\Question 15 6 7 Graph of f The graph of the piecewise-linear function f is shown in the figure. Let g be the inverse function of f. What is the maximum value of g? A B C 5 D 7Question 16 In a certain simulation, the population of a bacteria colony can be modeled using a geometric sequence, where the first day of the simulation is day 1. The population on day 4 was 4,000 bacteria, and the population on day 8 was 49,000 bacteria. What was the population of the colony on day 6 based on the simulation? A 26,500 B 26,192 C 14,000 D 611Question 17 The function f is given by f(I) = 5 . (0.7)". Which of the following describes f? A The function f models exponential decay and lim f(I) = 0. I-100 B The function f models exponential decay and lim f( I) = co. C The function f models exponential growth and lim f(x) = 0. I 100 D The function f models exponential growth and lim f () = co.Question 18 f(I) -2 10 -1 15 1 40 2 56 The table presents values for a function f at selected values of r. An exponential regression y = ab" is used to model these data. What is the value of f(1.5) predicted by the exponential function model? A 46.767 B 47.342 C 47.800 D 47.917Question 19 Number of Vehicles (thousands) Year 1996 265.0 1998 295.0 2000 394.7 2002 471.1 2004 565.5 2006 634.6 2008 775.7 2010 938.6 The table gives the number of alternative-fuel vehicles, in thousands, in use in the United States for selected years from 1996 to 2010. The function A defined by A(t) = - is used to model the data, in thousands, for 6