Math 1314 Departmental Final Exam Review (Fall 2021) PDF

MATH 1314 - Departmental Final Exam Review List the intercepts for the graph of the equation. 1) x2 + y - 36 = 0 2) 16x2 + y2 = 16 3) y = x2 + 14x + 48 Find an equation for the line, in the indicated form, with the given properties. 4) Containing the points (-2, 2) an...

MATH 1314 - Departmental Final Exam Review List the intercepts for the graph of the equation. 1) x2 + y - 36 = 0 2) 16x2 + y2 = 16 3) y = x2 + 14x + 48 Find an equation for the line, in the indicated form, with the given properties. 4) Containing the points (-2, 2) and (7, -4); slope-intercept form Write an equation for the line described. Write the equation in the form specified. 5) Through (3, 4), parallel to y + 8x = 4, Find an equation for the line with the given properties. 1 6) Perpendicular to the line y = x + 9; containing the point (4, -5) 9 Write the standard form of the equation of the circle with radius r and center (h, k). 7) r = 10; (h, k) = (1, -9) 8) r = 17; (h, k) = (-9, 8) Find the center (h, k) and radius r of the circle with the given equation. 9) (x - 6)2 + (y + 9)2 = 144 10) x2 + y2 - 6x - 16y + 73 = 16 Find the value for the function. x2 - 4 11) Find f(-2) when f(x) =. x+3 Find the domain of the function. x-3 12) h(x) = 3 x - 81x 13) f(x) = x2 + 4 14) f(x) = 7-x Revised Fall 2021 - page 1 The graph of a function f is given. Use the graph to answer the question. 15) Use the graph of f given below to find f(40). 50 -50 50 -50 Determine algebraically whether the function is even, odd, or neither. 16) f(x) = -3x4 - x2 17) f(x) = 4x3 + 5 x 18) f(x) = x2 - 3 Use the graph to find the intervals on which it is increasing, decreasing, or constant. 19) Find the average rate of change for the function between the given values. 20) f(x) = 4x3 - 8x2 - 1; from 1 to 5 page 2 Graph the function. 21) f(x) = x - 1 if x < 1 4 if x 1 22) f(x) = -x + 3 if x < 2 2x - 3 if x 2 Using transformations, sketch the graph of the requested function. 23) The graph of a function f is illustrated. Use the graph of f as the first step toward graphing the function F(x), where F(x) = f(x + 2) - 1. Find the vertex and axis of symmetry of the graph of the function. 24) f(x) = x2 + 4x + 3 page 3  25) f(x) = -x2 + 6x Solve the problem. 26) A projectile is thrown upward so that its distance above the ground after t seconds is h = -10t2 + 440t. After how many seconds does it reach its maximum height? 27) The manufacturer of a CD player has found that the revenue R (in dollars) is R(p) = -5p2 + 1200p, when the unit price is p dollars. If the manufacturer sets the price p to maximize revenue, what is the maximum revenue to the nearest whole dollar? Solve the inequality. 28) x2 + 3x - 28 > 0 For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at each x -intercept. 29) f(x) = 5(x - 6)(x + 1)4 30) f(x) = 5(x2 + 5)(x + 6)2 Use the Factor Theorem to determine whether x - c is a factor of f(x). 31) f(x) = 8x4 + 31x3 - 4x 2 + x - 4; x + 4 32) f(x) = 5x4 + 14x3 - 3x 2 + x + 3; x + 3 List the potential rational zeros of the polynomial function. Do not find the zeros. 33) f(x) = 6x4 + 2x3 - 3x2 + 2 Find the real solutions of the equation. 34) x3 + 4x2 - 4x - 16 = 0 35) x4 - 21x2 - 100 = 0 Use the given zero to find the remaining zeros of the function. 36) f(x) = x4 - 5x2 - 36; zero: -2i 37) f(x) = x3 + 8x2 + 25x + 26; zero: -3 + 2i 38) f(x) = x3 - 3x2 - 5x + 39; zero: -3 Find the vertical asymptotes of the rational function. x+6 39) g(x) = x2 - 64 page 4  x+2 40) h(x) = x2 + 49 Give the equation of the horizontal asymptote, if any, of the function. x+7 41) g(x) = x2 - 36 -x2 + 16 42) f(x) = x2 + 5x + 4 4x 5 - 2 43) f(x) = x - x3 The graph of a function f is given. Use the graph to answer the question. 44) For what numbers x is f(x) > 0? 25 -25 25 -25 For the given functions f and g, find the requested composite function value. 45) f(x) = 2x + 2, g(x) = 2x2 + 1; Find (f f)(0). 46) f(x) = x + 1, g(x) = 2x; Find (f g)(4). For the given functions f and g, find the requested composite function. 47) f(x) = x2 + 2, g(x) = x2 + 4; Find (f g)(x). page 5 Use the graph of the given one-to-one function to sketch the graph of the inverse function. For convenience, the graph of y = x is also given. 48) The function f is one-to-one. Find its inverse. 49) f(x) = 6x + 3 50) f(x) = (x + 2)3 - 8. Change the exponential expression to an equivalent expression involving a logarithm. 2 51) 4 = x Change the logarithmic expression to an equivalent expression involving an exponent. 2 52) logb 49 = 3 Find the domain of the function. 53) f(x) = log(x + 4) Write as the sum and/or difference of logarithms. Express powers as factors. x-1 54) log 2 x6 3 x 5y8 55) logb z2 Express as a single logarithm. 56) 4 log t - log s b b 57) log 5 + log (x3 - 4) + log 2 a a a page 6  1 1 58) 3 log 2 + log (x - 3) - log x 7 4 7 2 7 Solve the equation. 59) 4 x = 64 1 60) 2 x = 8 (1 + 2x) 61) 4 = 1024 62) log (3x) = log 4 + log (x - 3) 63) log3 x + log3(x - 24) = 4 64) log2(3x - 2) - log2(x - 5) = 4 Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. (4x - 1) 65) 3 = 13 Solve the system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. 66) 5x + 4y = 1 6x - 2y = -26 67) -2x - 3y = 8 2x + 3y = -9 page 7 Answer Key Testname: 1314 - DEPT FINAL - REVIEW-FA21 1) (-6, 0), (0, 36), (6, 0) 2) (-1, 0), (0, -4), (0, 4), (1, 0) 3) (-8, 0), (-6, 0), (0, 48) 2 2 4) y = - x + 3 3 5) y = - 8x + 28 6) y = - 9x + 31 7) (x - 1)2 + (y + 9)2 = 100 8) (x + 9)2 + (y - 8)2 = 17 9) (h, k) = (6, -9); r = 12 10) (h, k) = (3, 8); r = 4 11) 0 12) {x|x -9, 0, 9} 13) all real numbers 14) {x|x 7} 15) 20 16) even 17) neither 18) odd 19) Decreasing on - , - and , ; increasing on - , 2 2 2 2 20) 76 21) 22) page 8 Answer Key Testname: 1314 - DEPT FINAL - REVIEW-FA21 23) 24) (-2, -1); x = -2 25) (3, 9); x = 3 26) 22 sec 27) $72,000 28) (- , -7) or (4, ) 29) 6, multiplicity 1, crosses x-axis; -1, multiplicity 4, touches x-axis 30) -6, multiplicity 2, touches x-axis 31) No 32) Yes 1 1 1 2 33) ± , ± , ± , ± , ± 1, ± 2 6 3 2 3 34) {-4, -2, 2} 35) {-5, 5} 36) 2i, 3, -3 37) -3 - 2i, -2 38) 3 + 2i, 3 - 2i 39) x = -8, x = 8 40) none 41) y= 0 42) y = -1 43) no horizontal asymptotes 44) [-25, -15), (17.5, 25) 45) 6 46) 3 47) x4 + 8x2 + 18 page 9 Answer Key Testname: 1314 - DEPT FINAL - REVIEW-FA21 48) x-3 49) f-1 (x) = 6 3 50) f-1 (x) = x + 8 - 2 51) log 4 x = 2 52) b2/3= 49 53) (-4, ) 54) log 2 (x - 1) - 6 log 2 x 5 8 2 55) logb x + logb y - logb z 3 3 3 t4 56) log b s 57) log a ( 10x3 - 40) 4 8 x-3 58) log7 x 59) {3} 60) {-3} 61) {2} 62) 12 63) {27} 64) {6} 65) {0.83} 66) x = -3, y = 4; (-3, 4) 67) inconsistent page 10