MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. B) 6x + 4

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1 Math1420 Review Comprehesive Final Assessment Test Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Add or subtract as indicated. x + 5 1) x2 + 8x x - 1 x2 + 9x + 14 A) 6x2 + 41x + 29 (x - 2)(x - 6)(x - 7) B) 6x + 4 1) C) 6x2 + 41x + 29 (x + 2)(x + 6)(x + 7) D) 6x + 4 2x2 + 17x + 26 Solve the radical equation, and check all proposed solutions. 2) x - 3x - 2 = 4 2) A) {1, 2} B) {2, 9} C) {9} D) {-1} Solve the absolute value inequality. Other than, use interval notation to express the solution set and graph the solution set on a number line. 3) 3(x + 1) ) A) (-6, 4) B) [-8, 2] C) (-8, 2) D) [-6, 4] Determine whether the equation defines y as a function of x. 4) x = y2 4) A) y is a function of x B) y is not a function of x Evaluate the function at the given value of the independent variable and simplify. 5) f(x) = 4x2 + 5x - 6; f(x - 1) 5) A) 4x2-3x - 7 B) -3x2 + 4x - 7 C) 4x2-19x + 3 D) 4x2-3x + 3 1

2 Determine whether the given function is even, odd, or neither. 6) f(x) = x3 + x ) A) Even B) Neither C) Odd Evaluate the piecewise function at the given value of the independent variable. 7) g(x) = x2 + 5 x + 3 if x -3 ; g(-5) 7) x - 7 if x = -3 A) -5 B) - 15 C) 0 D) -12 Use the given conditions to write an equation for the line in slope-intercept form. 8) Passing through (1, -7) and (-1, 2) 8) A) y = 9 2 x B) y + 7 = - 9 (x - 1) 2 C) y = x D) y = mx Use the given conditions to write an equation for the line in the indicated form. 9) Passing through (2, 5) and perpendicular to the line whose equation is y = 1 6 x + 8; 9) slope-intercept form A) y = 6x - 17 B) y = - 6x - 17 C) y = - 6x + 17 D) y = x Find the average rate of change of the function from x1 to x2. 10) f(x) = 5x + 7 from x1 = -1 to x2 = 0 10) A) 1 2 B) 5 C) D) -28 2

3 Begin by graphing the standard quadratic function f(x) = x2. Then use transformations of this graph to graph the given function. 11) h(x) = -(x + 3) ) C) D) For the given functions f and g, find the indicated composition. 12) f(x) = -6x + 3, g(x) = 2x + 5 (g f)(x) A) -12x + 11 B) -12x + 33 C) -12x - 1 D) 12x ) Find the domain of the composite function f g. 13) f(x) = 2, g(x) = x ) x + 9 A) (-, -9) or (-9, ) B) (-, ) C) (-, -14) or (-14, ) D) (-, -9) or (-9, -5) or (-5, ) 3

4 Find the inverse of the one-to-one function. 14) f(x) = 3 x ) 1 A) f-1(x) = x3-8 B) f-1(x) = x C) f-1(x) = x - 8 D) f-1(x) = x3-8 Find the distance between the pair of points. 15) (3 7, -2) and (6 7, -1) 15) A) 8 B) 32 C) 7 D) 64 Complete the square and write the equation in standard form. Then give the center and radius of the circle. 16) x2 + y2-10x + 2y + 17 = 0 16) A) (x - 5)2 +(y + 1)2 = 9 (-5, 1), r = 3 C) (x - 5)2 +(y + 1)2 = 9 (5, -1), r = 9 B) (x - 5)2 +(y + 1)2 = 9 (5, -1), r = 3 D) (x + 5)2 +(y - 1)2 = 9 (-5, 1), r = 3 Find the coordinates of the vertex for the parabola defined by the given quadratic function. 17) f(x) = -7x2 + 14x ) A) (-2, -60) B) (2, -18) C) (1, 3) D) (-1, -25) Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the graph crosses the x-axis or touches the x-axis and turns around, at each zero. 18) f(x) = 1 4 x 2(x2-5)(x + 3) 18) A) 0, multiplicity 2, touches x-axis and turns around; -3, multiplicity 1, crosses x-axis B) 0, multiplicity 2, crosses x-axis; -3, multiplicity 1, touches x-axis and turns around; 5, multiplicity 1, touches x-axis and turns around; - 5, multiplicity 1, touches x-axis and turns around C) 0, multiplicity 2, touches x-axis and turns around; -3, multiplicity 1, crosses x-axis 5, multiplicity 2, touches x-axis and turns around D) 0, multiplicity 2, touches x-axis and turns around; -3, multiplicity 1, crosses x-axis; 5, multiplicity 1, crosses x-axis; - 5, multiplicity 1, crosses x-axis Use the Intermediate Value Theorem to determine whether the polynomial function has a real zero between the given integers. 19) f(x) = 9x5 + 10x3-5x2 + 7; between -1 and 0 19) A) f(-1) = -17 and f(0) = -7; no B) f(-1) = 17 and f(0) = 7; no C) f(-1) = -17 and f(0) = 7; yes D) f(-1) = 17 and f(0) = -7; yes Solve the problem. 20) Use synthetic division to divide f(x) = x3 + 1x2-26x + 24 by x + 6. Use the result to find all zeros of f. A) {6, -4, -1} B) {-6, 4, 1} C) {-6, -4, -1} D) {6, 4, 1} 20) 4

5 Find an nth degree polynomial function with real coefficients satisfying the given conditions. 21) n = 3; -1 and i are zeros; leading coefficient is 1 21) A) f(x) = x3 + 7x2 + 15x + 13 B) f(x) = x3 + 5x2 + 19x - 14 C) f(x) = x3 + 7x2 + 19x + 13 D) f(x) = x3-4x2 + 19x + 13 Use Descartes's Rule of Signs to determine the possible number of positive and negative real zeros for the given function. 22) f(x) = x5-2.7x x3 + 3x x ) A) 2 or 0 positive zeros, 3 or 1 negative zeros B) 3 or 1 positive zeros, 3 or 1 negative zeros C) 3 or 1 positive zeros, 2 or 0 negative zeros D) 2 or 0 positive zeros, 2 or 0 negative zeros Graph the rational function. x2 23) f(x) = x2 - x ) 5

6 C) D) Find the slant asymptote, if any, of the graph of the rational function. 24) f(x) = x 2-3x + 5 x + 4 A) y = x + 8 B) x = y + 3 C) y = x - 7 D) no slant asymptote 24) Solve the polynomial inequality and graph the solution set on a number line. Express the solution set in interval notation. 25) x2-7x ) A) [4, ) B) (-, 3] C) [3, 4] D) (-, 3] [4, ) 6

7 Solve the rational inequality and graph the solution set on a real number line. Express the solution set in interval notation. 1 26) x - 2 < 1 26) A) (-, 2) B) (-, 2) or (3, ) C) (-, 2] or [3, ) D) (2, 3) Graph the function. 27) Use the graph of f(x) = 3x to obtain the graph of g(x) = 3x ) 7

8 C) D) Find the domain of the logarithmic function. 28) f(x) = ln (8 - x) 28) A) (-, 8) B) (-, 0) C) (-, 8) or (8, ) D) (-8, ) Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. 29) log s2r A) C) 1 10 log log 3 s - 2 log 3 r B) log log 3 s - log 3 r 1 10 log log 3 s - log 3 r D) 10 log log 3 s - log ) Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions. 30) 1 5 (log 8 x + log8 y) - 5 log8 (x + 4) 30) A) log8 5 xy 5(x + 4) B) log8 5 xy (x + 4)5 C) log8 5 x + y (x + 4)5 D) log8 5 x + 5 y (x + 4)5 Solve the equation by expressing each side as a power of the same base and then equating exponents. 31) 125x = ) A) B) {-3} C) D) 1 6 Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. 32) e2x + ex - 6 = 0 32) A) 0.14 B) 0.69, 1.10 C) 0.69 D) 1.10,

9 Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic expressions. Give the exact answer. 33) log 4 (x + 2) - log 4 x = 2 33) A) {4} B) { 1 8 } C) { 2 } D) { } 34) ln (x - 6) + ln (x + 1) = ln (x - 15) 34) A) {-3} B) {3, -3} C) {3} D) Solve. 35) The function A = A0e x models the amount in pounds of a particular radioactive material stored in a concrete vault, where x is the number of years since the material was put into the vault. If 400 pounds of the material are placed in the vault, how much time will need to pass for only 50 pounds to remain? A) 360 years B) 190 years C) 180 years D) 185 years 35) Solve the problem. 36) Cindy will require $15,000 in 2 years to return to college to get an MBA degree. How much money should she ask her parents for now so that, if she invests it at 12% compounded continuously, she will have enough for school? (Round your answer to the nearest dollar.) A) $11,958 B) $11,799 C) $19,069 D) $ ) Solve the system by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets. 37) x 5 + y 15 = 1 37) x 3 - y 9 = 0 A) 15 2, 5 2 C) (x, y) x 5 + y = 1 D) 15 B) 5 2, 15 2 Solve the system of equations. 38) 2x + 4y + z = -3 3x - 4y - z = -22 2x + y + 2z = -3 A) {(3, 1, -5)} B) {(1, -5, 3)} C) {(-5, 1, 3)} D) {(-5, 3, 1)} 38) Solve the system by the addition(elimination) method. 39) 5x2-5y2 = -35 2x2 + 4y2 = 82 A) {(-3, -4), (-4, -3)} B) {(3, -4), (3, 4)} C) {(3, 4), (-3, 4), (3, -4), (-3, -4)} D) {(3, 4), (4, 3), (-3, -4), (-4, -3)} 39) 9

10 Solve by the method of your choice. 40) x2 + y2 = 20 (x - 8)2 + y2 = 20 A) {(2, 4), (2, -4), (-2, 4), (-2, -4)} B) {(4, 2), (4, -2)} C) {(2, 4), (2, -4)} D) {(4, 2), (4, -2), (-4, 2), (-4, -2)} 40) Graph the solution set of the system of inequalities or indicate that the system has no solution. 41) x + 3y -3 x > -3 y 6 41) C) D) 10

11 Solve the system of equations using matrices. Use Gaussian elimination with back-substitution. 42) x + y + z = 8 x - y + 5z = 26 5x + y + z = 28 A) {(4, -1, 5)} B) {(5, -1, 4)} C) {(4, 5, -1)} D) {(5, 4, -1)} 42) Solve the matrix equation for X. 43) 3-3 Let A = -8 0 and B = 4-1 A) X = B) ; 4X + A = B X = C) X = D) X = ) Find the product AB, if possible. 44) A = , B = A) C) B) D) ) 11

12 Graph the ellipse. 45) x y 2 64 = 1 45) C) D) 12

13 Graph the ellipse. 46) 9(x - 1)2 + 16(y - 2)2 = ) C) D) 13

14 Use vertices and asymptotes to graph the hyperbola. Find the equations of the asymptotes. 47) y x 2 25 = 1 47) A) Asymptotes: y = ± 2 5 x B) Asymptotes: y = ± 2 5 x C) Asymptotes: y = ± 5 2 x D) Asymptotes: y = ± 5 2 x 14

15 Use the center, vertices, and asymptotes to graph the hyperbola. 48) (x + 1) 2 - (y + 2) 2 = 1 48) 4 9 C) D) 15

16 Graph the parabola. 49) y2 = -12x 49) C) D) 16

17 Graph the parabola with the given equation. 50) (x + 1)2 = 5(y - 2) 50) C) D) 17

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