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MAC 1140 Module 5 Test Name___________________________________ MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine any local extrema and absolute extrema. 1) g(x) = |x| + 2 A) Local maximum: 2; absolute maximum: 2 C) Local minimum: -2; absolute minimum: -2 B) Local minimum: 0; absolute minimum: 0 D) Local minimum: 2; absolute minimum: 2 Answer: D Objective: (4.1) Find Extrema from Equation 2) Estimate graphically the local extrema of f(x) = 3x2 + 5x + 4. A) Local maximum: 1.92; no local minimum B) No local maximum; local minimum: -0.83 C) Local maximum: 1.92; local minimum: -0.83 D) No local maximum; local minimum: 1.92 Answer: D Objective: (4.1) Tech: Find Extrema 3) g(x) = -8x2 - 128x - 519 A) Local maximum: -7; absolute maximum: -7 C) Local minimum: -7; absolute minimum: -7 B) No local extrema; absolute maximum: -7 D) Local maximum: 7; absolute maximum: 7 Answer: A Objective: (4.1) Find Extrema from Equation 4) Use the graph of f to estimate the local extrema. y 4 3 2 1 -4 -3 -2 -1 1 2 3 4 x -1 -2 -3 -4 A) Local maximum: approx. 3.66; local minimum: approx. -2.55 B) No local maximum; no local minimum C) Local maximum: 1; local minimum: 4 D) Local maximum: ∞; local minimum: -∞ Answer: A Objective: (4.1) Find Extrema of Function from Graph 1 Use the graph of f to determine the intervals where f is increasing and where f is decreasing. 5) y 5x A) Decreasing on B) Decreasing on C) Decreasing on D) Decreasing on x≤ x≤ x≤ x≤ -2, increasing on -2 ≤ x ≤ 1, decreasing on x ≥ 1 -2, increasing on x ≥ -2 -2, increasing on -2 ≤ x ≤ 0, decreasing on 0 ≤ x ≤ 1, increasing on x ≥ 1 0, increasing on x ≥ 0 Answer: C Objective: (4.1) Find Where Function Increasing/Decreasing from Graph 2 Pick which graph satisfies the given conditions. 6) Polynomial of degree 3 with three distinct real zeros and a positive leading coefficient. y x A) B) y y x x C) D) y y x x Answer: C Objective: (4.2) Sketch Graph by Hand Given Properties, Degree Approximate the coordinates of each turning point by graphing f(x) in the standard viewing rectangle. Round to the nearest hundredth, if necessary. 7) f(x) = -7x2 + 16x - 5 A) (4.14, 1.14) B) (-1.14, 4.14) C) (1.14, 4.14) D) (1.14, -4.14) Answer: C Objective: (4.2) Tech: Find Turning Points 3 Graph the function. 8) f(x) = (-3x - 1)(x - 1)2 y x A) B) y y x x C) D) y y x x Answer: A Objective: (4.2) Tech: Graph Polynomial Function 4 The data table has been generated by a linear, quadratic, or cubic function f. All zeros of f are real numbers located in the interval [-3, 3]. By making a line graph of the data, conjecture the degree of f. x -3 -2 -1 0 1 2 3 9) f(x) -7 -5 -3 -1 1 3 5 y 8 6 4 2 -4 -3 -2 -1 -2 1 2 3 4 x -4 -6 -8 A) 1 B) 2 C) 3 D) 4 Answer: A Objective: (4.2) Determine Degree of Polynomial from Data Solve the problem. 10) A(x) = -0.015x3 + 1.05x gives the alcohol level in an average person's blood x hrs after drinking 8 oz of 100-proof whiskey. If the level exceeds 1.5 units, a person is legally drunk. Would a person be drunk after 6 hours? A) No B) Yes Answer: B Objective: (4.3) Solve Apps: Polynomial Equations Solve the polynomial equation graphically or numerically. Round to the nearest hundredth if necessary. 11) x3 - 48x - 128 = 0 A) -4, -4, 8 B) -8, -4, 4 C) 4, -4, 8 D) -4, 4, 8 Answer: A Objective: (4.3) Solve Polynomial Equation Graphically/Numerically Write the complete factored form of the polynomial f(x), given the indicated zero. 12) f(x) = 12x4 + 63x3 + 96x2 + 45x - 5 is a zero. 4 A) f(x) = 12x x - 5 4 x-1 x- 3 B) f(x) = 12x x + 5 4 C) f(x) = 12x x - 5 4 x+1 x+ 3 D) f(x) = x x + 5 4 Answer: B Objective: (4.3) Write Factored Form of Polynomial Given a Zero 5 x+1 x+ 3 x+1 x+ 3 Use the given information about a polynomial function f(x) to write its complete factored form. 13) f(x) = -6x2 + 18x + 108; zeros: 6 and -3 A) f(x) = 6(x - 6)(x + 3) B) f(x) = -6(x - 6)(x + 3) C) f(x) = (x - 6)(x + 3) D) f(x) = -6(x + 6)(x - 3) Answer: B Objective: (4.3) Write Factored Form of Polynomial Given Zeros Divide. Write with positive exponents. 7 2 14) 48x - 42x - 48x 6x A) 8x6 - 7x - 8 B) 48x6 - 42x - 48 C) 8x7 - 7x2 - 8x D) 8x7 - 42x2 - 48x C) 15 - 114i D) 111 - 30i C) 50i D) -50i Answer: A Objective: (4.3) Divide Polynomial by Monomial Multiply and write the result in standard form. 15) (7 - 8i)(9 - 6i) A) 15 + 114i B) 48i2 - 114i + 63 Answer: C Objective: (4.4) Multiply Complex Numbers Simplify the expression using the imaginary unit i. 16) -2500 A) ±50 B) i 50 Answer: C Objective: (4.4) Simplify Using the Imaginary Unit The graph and equation of a polynomial f(x) are given. Determine the number of real zeros and the number of imaginary zeros. 17) f(x) = x3 + 2x2 - 5x - 6 y 20 15 10 5 -4 -3 -2 -1 -5 1 2 3 4 x -10 -15 -20 A) Three real zeros; three imaginary zeros C) One real zero; two imaginary zeros B) Three real zeros; two imaginary zeros D) Three real zeros; no imaginary zeros Answer: D Objective: (4.4) Predict Number of Zeros Given Graph, Equation 6 Simplify the expression using the imaginary unit i. 18) (-5 + 9i) - 5 A) -10 + 9i B) 0 - 9i C) 0 + 9i D) 10 - 9i Answer: A Objective: (4.4) Add/Subtract Complex Numbers Find the complete factored form of the polynomial f(x) that satisfies the given conditions. 19) Degree 3, leading coefficient -4, zeros at 5, -3i, and 3i A) f(x) = -4(x + 5)(x2 + 9) B) f(x) = -4(x - 5)(x - 3i)(x + 3i) C) f(x) = -4(x - 5)(x2 + 9) D) f(x) = -4(x + 5)(x - 3i)(x + 3i) Answer: B Objective: (4.4) Find Factored Form Given Deg/Zeros/Lead Coefficient Multiply and write the result in standard form. 20) 3i(-1 - 8i)2 A) -48 - 189i C) -48i + 48i2 + 192i3 B) -189i D) -189 + 48i Answer: A Objective: (4.4) Multiply Complex Numbers 7