MA105 Final QUESTION 1 1. Select the correct description of right-hand and left-hand behavior of the graph of the polynomial function. Rises to the left, falls to the right Rises to the right, rises to the left Falls to the left, rises to the right Falls to the right Falls to the left, falls to the right 4 points QUESTION 2 1. Select the correct description of right-hand and left-hand behavior of the graph of the polynomial funciton. f(x) = 4x2 - 5x + 4 Falls to the left, rises to the right Falls to the left, falls to the right Rises to the left, rises to the right Rises to the left, falls to the right Falls to the left 4 points QUESTION 3 1. Find all the real zeroes of the polynomial function. f(x) = x2 - 25 -25 5 -5 25 5 4 points QUESTION 4 1. Use synthetic division to divide. (4x3 + x2 - 11x + 6) (x + 2) 4x2 - 5x - 6 4x2 - 7x + 3 4x2 - 2x - 2 4x2 + 5x - 12 4x2 + 7x - 4 4 points QUESTION 5 1. Use the Remainder Theorem and synthetic division to find the function value. Verify your answers using another method. h(x) = x3 - 6x2 - 5x + 7 h(-8) -849 -847 -851 -848 -845 4 points QUESTION 6 1. Find all the rational zeroes of the function. x3 - 12x2 + 41x - 42 -2, -3, -7 2, 3, 7 2, -3, 7 -2, 3, 7 -2, 3, -7 4 points QUESTION 7 1. The total revenue R earned (in thousands of dollars) from manufacturing handheld video games is given by R(p) = -25p2 + 1700p where p is the price per unit (in dollars). Find the unit price that will yield a maximum revenue. $38 $35 $36 $37 $34 4 points QUESTION 8 1. Find the domain of the function Domain: all real numbers x except x = 7 Domain: all real numbers x except x = 49 Domain: all real numbers x except x = 8 Domain: all real numbers x except x = -7 Domain: all real numbers x except x = 7 4 points QUESTION 9 1. Find the domain of the function and identify any vertical and horizontal asymptotes. Domain: all real numbers x Vertical asymptote: x = 0 Horizontal asymptote: y = 0 Domain: all real numbers x except x = 2 Vertical asymptote: x = 0 Horizontal asymptote: y = 0 Domain: all real numbers x except x = 5 Vertical asymptote: x = 0 Horizontal asymptote: y = 2 Domain: all real numbers x Vertical asymptote: x = 0 Horizontal asymptote: y = 2 Domain: all real numbers x except x = 5 Vertical asymptote: x = 5 Horizontal asymptote: y = 0 4 points QUESTION 10 1. Simplify f and find any vertical asymptotes of f. x+3; vertical asymptote: x = -3 x; vertical asymptote: none x; vertical asymptote: x = -3 x-3; vertical asymptote: none x2; vertical asymptote: none 4 points QUESTION 11 1. Determine the equations of any horizontal and vertical asymptotes of horizontal: y = 5; vertical: x = 0 horizontal: y = 1; vertical: x = -5 horizontal: y = 1; vertical: x = 1 and x = -5 horizontal: y = -1; vertical: x = -5 horizontal: y = 0; vertical: none 4 points QUESTION 12 1. Identify all intercepts of the following function. x-intercepts: (3, 0) no intercepts x-intercepts: (-3,0) x-intercepts: (0,0) x-intercepts: (3,0) 4 points QUESTION 13 1. Select the correct graph of the function. 4 points QUESTION 14 1. The game commission introduces 100 deer into newly acquired state game lands. The population N of the herd is modeled by where t is the time in years. Find the populations when t=40. (Round your answer to the nearest whole number.) 1,442 deer 1,632 deer 1,594 deer 1,550 deer 1,500 deer 4 points QUESTION 15 1. Evaluate the function at the indicated value of x. Round your result to three decimal places. Function: f(x) = 6000(6x) Value: x = -1.3 584.191 784.191 -584.191 684.191 -784.191 4 points QUESTION 16 1. Select the graph of the function. 4 points QUESTION 17 1. Use the One-to-One Property to solve the equation for x. ex2-6 = e5x x = -6 x=5 x = 6, -1 x = -6, -1 x = -6,1 4 points QUESTION 18 1. log366 = 1/2 36 = -6 36 = 6 6 = 36 36 = -1/6 36 = 1/6 4 points QUESTION 19 1. Write the exponential equation in logarithmic form. 272 = 729 log27729 = 2 log27729 = 1/2 log72927 = 2 log27729 = -2 log272 = 729 4 points QUESTION 20 1. Find the exact value of the logarighmic expression without using a calculator. 4 ln e7 7 28 4 e 1 4 points QUESTION 21 1. Condense the expression to the logarithm of a single quantity. ln310 + ln3x ln3(10 - x) ln310/x ln3(10 + x) ln310x ln310x 4 points QUESTION 22 1. Solve for x. 6x = 1,296 6 10 4 -6 -4 4 points QUESTION 23 1. Solve the exponential equation algebraically. Approximate the result to three decimal places. ex - 8 = 12 ln20 2.485 ln20 2.996 ln20 -2.485 ln20 2.079 ln20 -2.996 4 points QUESTION 24 1. An initial investment of $9000 grows at an annual interest rate of 5% compounded continuously. How long will it take to double the investment? 1 year 14.40 years 13.86 years 14.86 years 13.40 years 4 points QUESTION 25 1. The populations (in thousands) of Pittsburgh, Pennsylvania from 2000 through 2007 can be modele by where t represents the year, with t = 0 corresponding to 2000. Use the model to find the population in the year 2001. 2,418,774 2,419,774 2,421,774 2,420,774 2,422,774