Midterm Review (Honors Algebra 2) 4. Solve the compound inequality. Then graph its solution on a number line. 5 7 or 3x x

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Midterm Review (Honors Algebra ) Name Chapter & : Equations Inequalities, and Linear Functions. The graph of function f(x) is shown at right. Find f(3).. Evaluate f( ) when f ( x) x 5x. 3.

1 Midterm Review (Honors Algebra ) Name Chapter & : Equations Inequalities, and Linear Functions. The graph of function f(x) is shown at right. Find f(3).. Evaluate f( ) when f ( x) x 5x. 3. Solve the inequality ( x 4) 5x 4. Then graph its solution on a number line. 4. Solve the compound inequality. Then graph its solution on a number line. a. x 5 7 or 3x9 x b. 8 x A bag of lawn fertilizer claims that it will cover 5000 square feet of grass. Your yard is 7,500 square feet. If one bag of lawn fertilizer costs $8.96, then how much will it cost to fertilize your yard? 6. Solve the inequality x 5. Graph your results on a number line. 7. Identify the slope and y-intercept of the line whose equation is x3y. Then graph the line at right. 8. What is the equation of the line that passes through the point (, ) and has a slope of -? 9. What is the vertex of the graph of y x 4? 0. The graph at right shows the temperature change between 5am and 8pm. Find the temperature change from 5 am to :00 am.. Find the minimum and maximum values of the objective function C = x + 5y.

2 Chapter 4 Quadratic Functions. What is the vertex of the graph of y = x x + 9? 3. Fully factor 3x + 7x Fully factor 5x 7x What are the solutions of -x = -87? 6. Write the expression as a complex number in standard form: (- + i)( - i) 7. Simplify + i 3i 8. Solve the following equation: 6( u 5) 0 9. If x + 5x + c is a perfect square trinomial, what is the value of c? 0. Solve the equation x + 4x = -5 by completing the square.. What are the solutions of x + 0x + 04 = 0?

. With the quadratic formula, find the solutions of 5x + 9x = - x + 5x + 3. Consider the quadratic function f(x) = -3x + 7x -. Find the y intercept and the equation of the axis of symmetry. 4.

3 . With the quadratic formula, find the solutions of 5x + 9x = - x + 5x + 3. Consider the quadratic function f(x) = -3x + 7x -. Find the y intercept and the equation of the axis of symmetry. 4. A rocket is launched with an initial velocity of 94 feet per second from the top of a cliff 5 feet high. Its height is described by h(t) = -5t + 94t + 5. How long will the rocket take to hit the ground? 5. Johnson Manufacturing estimates that its profit P(in hundreds of dollars)after producing x thousand units can be expressed as P(x) = -x + 04x + 6. How many units must be produced to obtain the maximum profit? 6. Write the equation y = x 6x + 8 in vertex form and factored form. 7. Multiple Choice: Solve x + 6x = 6 by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are located. A), 3 B) between 4 and 3; between and C) 3 D) between 5 and 4; between and 8. Multiple Choice: What quadratic inequality is graphed? A) y (x+4)(x-3) B) y x - x - C) y x + x + D) y x - x -

4 Chapter 5: Polynomials and Polynomial Functions 9. What is the simplified form of 6xy xy 30. Subtract: (3x 3 + 0x + 5) - (x 3 4x + 6) 3. Add: (0x 3 + 7x ) + (x 3 - x + 7) 3. Simplify: (3x 5) Factor completely: 3x 4 + 9x 3 + x + 3x 34. Factor completely: 0x 3 + 0x Divide: (0x 4 + 5x 3 + 4x - 9) by (x + ) 36. Determine the end behavior of the function: f(x) = -4x 4 3x x + 5

37. Multiple Choice: Which cubic equation is graphed? A) y = (x + 4)(x + )(x ) 4 B) y = 4(x + 4)(x + )(x ) C) y = (x - 4)(x - )(x + ) 4 D) y = - (x + 4)(x + )(x ) 4 38.

5 37. Multiple Choice: Which cubic equation is graphed? A) y = (x + 4)(x + )(x ) 4 B) y = 4(x + 4)(x + )(x ) C) y = (x - 4)(x - )(x + ) 4 D) y = - (x + 4)(x + )(x ) Find all the roots of x 4 8x + x State the number of real zeros for the function whose graph is shown below: 40. Write an equation for a polynomial function with zeros at - and +3i. Chapter 8 Rational Functions 4. Simplify and reduce the rational expression. x y 3x z 9x z 4y Identify all horizontal and vertical asymptotes of the graph of the following function: 8 f ( x) x 4

6 43. What is the oblique asymptote for the function f(x) = x 4x+? x+ 44. Multiple Choice: What function matches the graph to the right? A) f(x) = + B) f(x) = x 3 x+3 C) f(x) = x+3 D) f(x) = x What are the domain and range of the function 8 f ( x) +? x Graph the rational function x 3x f(x). x 5x 4 x - 3x 47. Simplify the rational expression.. x 5x Simplify the rational expression. x 8x6 x 6x 8 x x Simplify the rational expression. 4x 3 x x. 50. Simplify: 6x 4 x 9 x3

7 5. Solve. x 3 x x 3 5. Perform the operations and simplify: x 3 5 x Simplify the expression 3 x 5 x x4 3x 4 x 4 3x6 54. Laurie can paint a fence in 7 hours and her friend Beth can paint a fence in 4 hours. How long will if take them if they paint the fence together. Bonus! 55. Graph the function x, if x 0 x 4, if x Which quadratic function CANNOT be represented by the graph shown? a. y x x 4 5 b. y ( x 5)( x ) c. y ( x 5)( x ) d. y ( x ) 9

8 57. Which cubic equation is graphed? a. b. y ( x 3)( x )( x ) y ( x 3)( x )( x ) c. y ( x 3)( x )( x ) d. y ( x 3)( x )( x ) 58. Divide 4 ( x 3x 8) by ( x ). 59. What is the graph of x 7x x 4? a. b. c. d. 60. Which rational function is graphed? a. x x 4 b. 7 ( x)( x4) c. 7 ( x)( x4) d. x 6x8 ( x)( x4) 6. Solve. 6. Identify all horizontal and vertical asymptotes of the function: x 4x x 3

9 63. What is the equation of the line that passes through the point (, ) and is parallel to the line 0x + 5y =? 64. The graph shows the temperature change between 5 am and 8 pm. Find the average rate of temperature change from 5 am to am. 65. Graph 0x + 5y >. 66. Find the range of the graph x, if x x, if x 67. Find the real zeros of the function f(x) = 4x x 0 using your graphing calculator. 68. A rocket is launched with an initial velocity of 94 feet per second from the top of a cliff 5 feet high. Its height is described by h(t) = 5t + 94t + 5 where t is the time in seconds and h(t) is the corresponding height in feet. The velocity of the object can be modeled by v = 3t + 94 where t is the time in seconds and v is the corresponding velocity of the object. With what velocity does the object hit the ground? 69. Simplify (x + )(0x 3 + 7x ) + (x 3 x + 7).

10 70. Completely factor 4x 6 + 4x 4 5x If you factor x 3 7 in the form (x a)(x + bx + c), what is the value of a? 7. Divide (x 4 + 3x 3 + x + 8x) by (x + x) using long division. 73. State the number of real zeros, type (quadratic, cubic, etc.), and sign of the leading coefficient for the function whose graph is shown at right. 74. Find the domain and range of the polynomial shown. 75. Given the graph, what is the solution to the inequality x 3 + 3x < 0? 76. If R is the total resistance for a parallel circuit with two resistors of resistances r and r, then R = r + r. Find the resistance r if the total resistance R is 30 ohms and r is 8 ohms. 77. Given the function f(x) = 3x x+5, find lim x f(x).

MAT 107 College Algebra Fall 2013 Name. Final Exam, Version X

MAT 107 College Algebra Fall 2013 Name. Final Exam, Version X MAT 107 College Algebra Fall 013 Name Final Exam, Version X EKU ID Instructor Part 1: No calculators are allowed on this section. Show all work on your paper. Circle your answer. Each question is worth