MATH 1314 Test 2 Review

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Name: Class: Date: MATH 1314 Test 2 Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Find ( f + g)(x). f ( x) = 2x 2 2x + 7 g ( x) = 4x 2 2x + 9 A. ( f + g)(x) = 6x 2 + 4x 16 B. ( f + g)(x) = 6x 4 4x 2 + 16 C. ( f + g)(x) = 2x 4 2 D. ( f + g)(x) = 6x 2 4x + 16 E. ( f + g)(x) = 2x 2 2 2. Find ( f / g )(x). f ( x) = x 2 + 7x g ( x) = 2 x A. Ê Á f / gˆ ( x) = x 2 + 7x 2 x, x 2 B. Ê Á f / gˆ ( x) = x 2 + 7x 2 x, x 2 C. Ê Á f / gˆ ( x) = x + 7 2, x 0 D. Ê Á f / gˆ ( x) = x 2 + 7x 2 x, x 0 E. Ê Á f / gˆ ( x) = x 2 2 7, x 0 3. Evaluate the indicated function for f ( x) = x 2 7 and g ( x) = x + 3. Ê Á f gˆ ( t + 2) A. t 2 + 3t 2 B. t 2 t 8 C. t 2 + t 8 D. t 2 + t 2 E. t 2 + 3t 8 1

Name: 4. Evaluate the indicated function for f ( x) = x 2 3 and g ( x) = x + 7. ( fg )(1) A. 30 B. 20 C. 16 D. 12 E. 32. Find f û g. f ( x) = 2x + 7 g ( x) = x + 2 A. Ê Á f û gˆ ( x) = 3x + 9 B. Ê Á f û gˆ ( x) = 2x 2 + 3x + 14 C. Ê Á f û gˆ ( x) = 2x + 3 D. Ê Á f û g ˆ ( x) = 3x + E. Ê Á f û gˆ ( x) = 2x + 9 6. Find the inverse function of f. f ( x) = x + 2 A. f 1 ( x) = x + 2 B. f 1 ( x) = x 2 C. f 1 ( x) = x 2 D. f 1 ( x) = x + 2 E. f 1 ( x) = x + 2 2

Name: 7. Find the standard form of the quadratic function shown below: A. f ( x) = ( x + 1) 2 B. f ( x) = 3( x + 1) 2 C. f ( x) = ( x 1) 2 D. f ( x) = 3( x 1) 2 E. f ( x) = x 2 + 1 8. From the graph of the quadratic function f ( x) = ( x + 2) 2 9, determine the equation of the axis of symmetry. A. x = 9 B. x = 9 2 C. x = 2 D. x = 9 E. x = 2 9. Determine the x-intercept(s) of the quadratic function f ( x) = x 2 + 4x 32. A. ( 4, 0), ( 8, 0) B. no x-intercept(s) C. ( 0, 0), ( 7, 0) D. ( 4, 0), ( 8, 0) E. ( 0, 0), ( 7, 0) 3

Name: 10. Determine the vertex of the graph of the quadratic function f ( x) = x 2 + x + 4. Ê 1 A. 4, 3 ˆ Á 4 Ê ˆ B. 1, Á 4 Ê 1 C. 2, ˆ Á 4 Ê 1 D. Á 2, 1 ˆ Ê 1 E. 2, 3 ˆ Á 2 11. Write the quadratic function f ( x) = x 2 4x + 3 in standard form. A. f ( x) = ( x + 1) + 2 B. f ( x) = ( x + 2) + 1 C. f ( x) = ( x + 1) 2 D. f ( x) = ( x 2) 1 E. f ( x) = ( x 2) + 1 4

Name: 12. Match the equation with its graph. f ( x) = 1 Ê 20 x x 4 x 3 x 2 6x Á A. D. ˆ B. E. C. 13. Describe the right-hand and the left-hand behavior of the graph of n x ( ) = x 4 + 10x 3 7. A. Because the degree is odd and the leading coefficient is negative, the graph rises to the left and rises to the right. B. Because the degree is even and the leading coefficient is negative, the graph rises to the left and falls to the right. C. Because the degree is even and the leading coefficient is negative, the graph falls to the left and falls to the right. D. Because the degree is even and the leading coefficient is negative, the graph falls to the left and rises to the right. E. Because the degree is even and the leading coefficient is negative, the graph rises to the left and rises to the right.

Name: 14. Describe the right-hand and the left-hand behavior of the graph of t( x) = 4x 7x 3 13. A. Because the degree is odd and the leading coefficient is positive, the graph rises to the left and falls to the right. B. Because the degree is odd and the leading coefficient is positive, the graph falls to the left and falls to the right. C. Because the degree is even and the leading coefficient is positive, the graph rises to the left and rises to the right. D. Because the degree is odd and the leading coefficient is positive, the graph rises to the left and rises to the right. E. Because the degree is odd and the leading coefficient is positive, the graph falls to the left and rises to the right. 1. Find all real zeros of the polynomial f ( x) = x 3 6x 2 9x + 4 and determine the multiplicity of each. A. x = 6, multiplicity2; x = 3, multiplicity1 B. x = 3, multiplicity 2; x = 6, multiplicity1 C. x = 3, multiplicity 1; x = 3, multiplicity1; x = 6, multiplicity1 D. x = 3, multiplicity1; x = 6, multiplicity1; x = 6, multiplicity 1 E. x = 6, multiplicity 3 16. Find all real zeros of the polynomial f ( x) = x 4 + x 3 + 6x 2 and determine the multiplicity of each. A. x = 0, multiplicity 2; x = 3, multiplicity1; x = 2, multiplicity1 B. x = 3, multiplicity2; x = 2, multiplicity2 C. x = 3, multiplicity2; x = 2, multiplicity2 D. x = 0,multiplicity 1;x = 3,multiplicity 1;x = 3,multiplicity 1; x = 2,multiplicity1 E. x = 0, multiplicity 2; x = 3, multiplicity1; x = 2, multiplicity 1 17. Use long division to divide. Ê x 3 + x 2 ˆ + 16x + 80 Á ( x + ) A. x 2 + 16 B. x 2 + 10x + 66 + 90 x + C. x 2 + 10x + 46 D. x 2 + 10x + 46 246 x + E. x 2 + 20 6

Name: 18. Use long division to divide. Ê x 3 ˆ + 8 Á ( x + 2) A. x 2 + 2x 4 B. x 2 4 C. x 2 + 4 D. x 2 2x + 4 E. x 2 2 4 + x + 2 19. Use synthetic division to divide. Ê 24 + x 3 + 22x 27x 2 ˆ Á ( x 2) A. x 2 17x 12 B. x 2 7x + 1 C. x 2 22x + 8 D. x 2 7x 20 E. x 2 + 11x 6 20. If f ( x) = 3x 2 4x + 1, use synthetic division to evaluate f ( 4). A. f ( 4) = 27 B. f ( 4) = 63 C. f ( 4) = 31 D. f ( 4) = 33 E. f ( 4) = 31 21. If x = 1 is a root of x 3 + 4x 2 x 4 = 0, use synthetic division to factor the polynomial completely and list all real solutions of the equation. A. ( x + 4) ( x + 1) 2 ; x = 4, 1 B. ( x + 4) ( x + 1) ( x 1); x = 4, 1, 1 C. ( x + 4) ( x 4) ( x 1); x = 4, 4, 1 D. ( x + 4) ( x + 1); x = 4, 1 E. ( x 4) ( x + 1) ( x 1); x = 4, 1, 1 7

Name: 22. Using the factors ( x + ) and ( x + 2), find the remaining factor(s) of f ( x) = x 3 + 6x 2 + 3x 10 and write the polynomial in fully factored form. A. f ( x) = ( x + ) ( x + 2) ( x + 1) B. f ( x) = ( x + ) ( x + 2) C. f ( x) = ( x + ) ( x + 2) ( x 1) D. f ( x) = ( x + ) ( x + 2) E. f ( x) = ( x + ) ( x + 2) ( x + 3) 23. Using the factors ( 3x + 2) and ( x 1), find the remaining factor(s) of f( x) = 6x 4 + 23x 3 12x 2 11x + 6 and write the polynomial in fully factored form. A. f ( x) = ( 3x + 2) ( x 3) 2 ( x + 1) B. f ( x) = ( 3x + 2) ( 3x + 2) ( 2x 1) ( x 1) C. f ( x) = ( 3x + 2) ( x + 3) ( 2x 1) ( x 1) D. f ( x) = ( 3x + 2) ( 2x 1) ( x + 1) E. f ( x) = ( 3x + 2) ( x 1) 24. Find all zeros of the function f ( x) = ( x + 2) ( x + 3i) ( x 3i). A. x = 2 B. x = 2, 3i, 3i C. x = 2, 3, 3 D. x = 2, 3i, 3i E. x = 2, 3i È 2. Find all zeros of the function f ( x) = ( x 4) ( x + 3) ÎÍ x + ( 4 + 3i) A. x = 4, 3, 4 + 3i, 4 + 3i B. x = 4, 3, 4 3i, 4 + 3i C. x = 4, 3, 4 + 3i, 4 3i D. x = 4, 3, 4 3i, 4 3i E. x = 4, 3, 4 3i, 4 + 3i È ÎÍ x ( 4 3i). 26. Given i is a root, determine all other roots of f ( x) = x 3 + x 2 + 2x + 12. A. x =, i B. x = ±, i C. x = ±, D. x =, ± i E. x =, ± 8

Name: 27. Find all the real zeros of f ( x) = 4x 3 20x 2 23x 6. A. x = 1 3, 1 6 B. x = 1 2, 6 C. x = 1 2, 1 6 D. x = 1 6, 2 E. x = 1 2, 6 28. Write f ( x) = x 3 4x 2 + 4x 16 as a product of linear factors. A. x = ( x 4) ( x + 2i) ( x 2i) B. x = ( x 4) ( x 2) C. x = ( x 4) ( x 2i) D. x = ( x 4) ( x + 2) E. x = ( x + 4) ( x 4) ( x + 2) 9

MATH 1314 Test 2 Review Answer Section MULTIPLE CHOICE 1. ANS: D PTS: 1 REF: 46 OBJ: Find combinations of functions 2. ANS: A PTS: 1 REF: 49 OBJ: Find combinations of functions 3. ANS: E PTS: 1 REF: 1 OBJ: Evaluate combinations of functions 4. ANS: C PTS: 1 REF: 0 OBJ: Evaluate combinations of functions. ANS: C PTS: 1 REF: 2 OBJ: Find compositions of functions 6. ANS: C PTS: 1 REF: 60 OBJ: Find inverse of functions 7. ANS: D PTS: 1 REF: 78 OBJ: Determine the standard form of a quadratic function 8. ANS: C PTS: 1 REF: 71 OBJ: Determine axis of symmetry 9. ANS: D PTS: 1 REF: 74 OBJ: Determine x-intercepts of quadratic function 10. ANS: D PTS: 1 REF: 70 OBJ: Determine vertex of quadratic function 11. ANS: D PTS: 1 REF: 76 OBJ: Write quadratic function in standard form 12. ANS: A PTS: 1 REF: 86 OBJ: Match polynomial and graph 13. ANS: C PTS: 1 REF: 88 OBJ: Determine right/left-hand behavior of polynomial 14. ANS: E PTS: 1 REF: 87 OBJ: Determine right/left-hand behavior of polynomial 1. ANS: C PTS: 1 REF: 90 OBJ: Determine zeros and multiplicity 16. ANS: E PTS: 1 REF: 92 OBJ: Determine zeros and multiplicity 17. ANS: A PTS: 1 REF: 98 OBJ: Divide polynomials using long division 18. ANS: D PTS: 1 REF: 99 OBJ: Divide polynomials using long division 19. ANS: A PTS: 1 REF: 103 OBJ: Divide polynomials using synthetic division of polynomial 20. ANS: B PTS: 1 REF: 109 OBJ: Evaluate using synthetic division 21. ANS: B PTS: 1 REF: 111 OBJ: Factor using synthetic division 22. ANS: C PTS: 1 REF: 114 OBJ: Factor polynomial given factor(s) 23. ANS: C PTS: 1 REF: 11 OBJ: Factor polynomial given factor(s) 24. ANS: B PTS: 1 REF: 120 OBJ: Determine zeros of polynomial 2. ANS: D PTS: 1 REF: 121 OBJ: Determine zeros of polynomial 26. ANS: A PTS: 1 REF: 129 OBJ: Approximate zeros with graphing utility 27. ANS: B PTS: 1 REF: 138 OBJ: Determine zeros of a function 28. ANS: A PTS: 1 REF: 132 OBJ: Approximate zeros with graphing utility 1

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