( ) = 2 x + 3 B. f ( x) = x 2 25

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1 PRACTICE - Algebra Final Exam (Semester 1) - PRACTICE 1. Which function contains only a vertical translation? A. f x ( ) = x + 3 B. f ( x) = x 5 C. f ( x) = 1( x 9) D. f ( x) = x + 4. Which function is a reflection over the x-axis, horizontal translation of 4 units to the left, and up 6 units. A. f x = (x + 4)! + 6 B. f x = (x 4)! 6 C. f x = ( x + 4)! + 6 D. f x = ( x 4)! 6 3. Let f ( x) = 6( x + 5) +. Which of the following functions is a reflection in the y-axis of the graph of f? A. g( x) = 6( x 5) B. g( x) = 6( x + 5) C. g( x) = 6( x + 5) D. g( x) = 6( x + 5) 4. Write a function g whose graph represents a translation 3 units up of f(x) = x - 9. A. f(x) = x +3 B. f(x) = 5x - 9 C. f(x) = x - 6 D. f(x) = x The function g x ( ) = 1 3 x + 5 is a combination of transformations of f( x) x. letter describes the transformation. = Choose which A. vertical shift 5 units down, horizontal shift units right, vertical shrink by a factor of 1 3 B. horizontal shift units right, vertical stretch by a factor of 3, vertical shift 5 units down C. horizontal shift units left, vertical stretch by a factor of 3, vertical shift 5 units down D. horizontal shift units left, vertical shrink by a factor of 1, vertical shift 5 units down 3 6. Which equation has a graph that is a line passing through the point ( 3, 8) and is parallel to the graph of y = 3 x 5? A. y = 3 x + 10 B. y = 3 x 8 C. y = 3 x + 8 D. y = 3 x 10

2 7. The data pairs ( x, y) represent the number of people y in the store x minutes after the store opens. Write a linear equation to fit this data and interpret the slope and y-intercept. ( 0, 75 ), ( 1, 99 ), (, 13 ), ( 3, 147 ), ( 4, 171 ), ( 5, 195 ) A. Initially there were 75 people in the store and about 4 people entered the store each minute. B. Initially there were 75 people in the store and about 100 people entered the store each minute. C. Initially there were people in the store and about 75 people entered the store each minute. D. Initially there were 0 people in the store and about 4 people entered the store each minute. 8. Evaluate the polynomial for the given value: f x = 4x! + 7x! 8; x = 3 A. f(-3) =-179 B. f(-3) = 163 C. f(-3) = -53 D. None of the above 9. Solve the system of linear equations. 3x - 9y + 7z = -1-4x + 5y - z = 5-11x + y + 1z = -53 A. (15, 19, 15) B. (-, -3, -6) C. No solutions D. Infinite Solutions 10. You and your friend are playing water volleyball. The parabola shows the path of your friend s serve. The path of your serve can be modeled by the function h x ( ) = 1x + 4x 6. Choose the correct inequality symbol to indicate whose serve travels higher. maximum height of your serve maximum height of your friend s serve A. > B. < C. D. =

3 11. You help setup a dance to help raise money for your school club. The organizers of the dance spend $85 to get everything setup. The table below shows the profits y (in dollars) when x tickets are sold for the dance. What is the cost per ticket? Tickets, x Profit, y A. $1.00 B. $1.0 C. $1.40 D Which of the following parabolas has a vertex at (0, -7)? A. y = (x 7)! B. focus: ( 0, 7); directrix: y = 7 C. y = 1 6 x 7 D. y = ( 5 x 7 ) Let gx ( ) = f( x) and hx ( ) = f( x). For which of the following functions is gx ( ) = hx ( )? f x A. ( ) C. f( x) = x B. f x ( ) = x + 3 = x D. f ( x) = x 14. Let the graph of g represent a translation right and up of the graph of f( x) x. following is a possible equation? A. g(x) = x 4 B. g(x) = (x 5) +6 C. g(x) = (x + 1) 8 D. g(x) = (x + 7) = Which of the 15. The Gree-D cable company charges $30 per month plus a setup fee of $75. The SuperSlo cable company charges $40 per month, but due to a special promotion is not currently charging a setup fee. Write an equation for the Gree-D cable company modeling the total cost y for a subscription lasting x months. A. y = 30x +75 B. y = 30x + 40 C. y = 40x D. y = 75x Which inequality is shown in the graph? A. y < x + 3x + 4 B. y < x 3x + 4 C. y x + 3x + 4 D. y x 3x + 4

4 17. Classify the function by its function family. f(x) = x - 30 A. constant B. quadratic C. absolute value D. linear 18. What is the vertex and directrix of the given function: y =!!" x!? A. Vertex: (0,0); directrix: y = -16 B. Vertex: (0,-16); directrix: y = 16 C. Vertex: (0,0); directrix: y = 16 D. Vertex: (0,16); directrix: y = Choose the function that has a focus 1 unit above the vertex at ( 4, ). A. f(x) = ¼(x 4) B. f(x) = 1(x 4) - C. f(x) = ⅛(x + 4) D. f(x) = 1(x + 4) - 0. Which of the following values are x-coordinates of the solutions of the system? y = x + 4x 15 y = 3x + 5 A. -5,-10 B. -10 and 17 C. -5 and 4 D. 4 and The table shows the height of the water in a tank where water is being added at a constant rate. How long will it take for the height of the water in the tank to be 40 feet? A. 95 hours B. 100 hours Time (hours), t Height (feet), y C. 105 hours D. 110 hours. Factor x 8x 0 completely. Which of the following is one of the factors? A. x B. x +8 C. x 8 D. x + 3. Factor 3x + 13x + 14 completely. Which of the following is one of the factors? A. 3x+ 7 B. x- C. x + 7 D. x Factor 9x +30x + 5 completely. Which of the following is one of the factors? A. 9x 3 B. 3x + 5 C. 3x 4 D. Does not factor

5 5. Factor x 4 56 completely. Which of the following is one of the factors? A. x + 4 B. x 56 C. x 16 D. x-8 6. Find the zeros of the function f(x) = x A. 4i, -4i B. 4, 4 C. 16, 16 D. 16i, 16i 7. Perform the operation. ( + 3i)(-4 + 5i) A i B. 13-8i C. -3-i D. None of the above 8. Solve x - x - 8 = 0 A. x =, x = -4 B. x = -, x = 4 C. x = -, x = -8 D. x =, x = Find the vertex of: y = x + 8x. A. (4, 50) B. (-, -10) C. (-4, -14) D. None of the above 30. A ball is tossed in the air so that its height h (in feet) after t seconds can be modeled by the function h(t) = -18t + 40t -3. What is the height of the balloon after 1 second? A. 61 feet B. 55 feet C. 5 feet D. 19 feet 31. Solve -x + x = -16. A. x = 1 ± 17 B. x = 1 ± 5 C. x = ± 17 D. x = ± 5

6 3. Determine the number of solutions of the quadratic equation: y = 3x + 6x + 8. A. 3 B. C. 1 D Which is a factor of the polynomial: f x = x! + 37x 84? A. (x -7) B. (x 3) C. (x +3) D. (x + 4) 34. Analyze the graph of the polynomial function and choose the correct statement. A. The degree is at least 3 because there are 3 turning points. B. There are 5 zeros and the degree is odd. C. The leading coefficient is negative and the degree is even. D. The leading coefficient is positive and there are turning points. 35. Which statement about the graph of 4( y + 4) = ( x ) is not true? A. The vertex is (, 4). B. The axis of symmetry is x =. C. The focus is (, 5). D. The graph represents a function. 36. Classify the function. y = -4x 5 A. even B. odd C. neither D. linear 37. Choose the correct function that represents the graph. A. x ( ) = x B. f( x) = x + 3 C. f( x) x 3 = D. f x ( ) = x The area of the rectangle is 64 square centimeters. Find the value of x. A. 3 B. 8 C. 64 D. 16

7 39. Find the inverse of the function: y = x 11 A. y = ± x + 11 B. y = ± x 11 C. y = ± x 11 D. y = ± x What is the solution of the inequality 0 3 x 5 >? A. x > 41 B. x < 41 C. 1<x<41 D. None of the above 41. Which function does the graph represent? A. B. C. y y y ( x ) = 1 = + x 1 ( x ) = 1 D. y = + x 1 4. Let f ( x) = 4x + 5, g( x) = 1x 3x 3 +, and hx ( ) = 8x 9x+ 3. Find ( f + g)( x) A. -3x + 5x + 7 B. 3x + 3x + 7 C. 3x + 5x + 3 D. -3x + 3x Let f ( x) = 6x + 8, g( x) = 3x 8x + 4, and h( x) = x 3 4x + 1. Find ( g h)( x) A. x! 8x! + 7x + 5 B. x! 8x! + 7x + 3 C. x! 8x! 7x + 3 D. x! 8x! + 7x Let f( x) = x + 3, g( x) = 7x 4x +, and hx ( ) = 8x 9x+ 3. Find ( fg)( x ) A. 14x 3-6x + 17x + 5 B. -8x 3 + x + 5x + 6 C. -4x x + 6 D. -8x 3 - x + 5x - 5

8 45. Choose the easiest and fastest method to solve the quadratic equation. ( x 5) = 36 A. quadratic equation B. factoring C. square root D. It cannot be solved. 46. The daily temperature in the month of May 016 is listed in the table below where d is the day in May and t is the temperature in Fahrenheit. What type of relationship does the data show? Day, d Temp, t A. linear B. quadratic C. exponential D. no relationship Simplify the expression. 8i 16! A. 6 B. 170 C. Already Simplified D. None of the above 48. Write the expression in simplest form. 3 7x 6 A. 9x 6 B. 3x C. 9x 3 D. 3x Simplify the expression.! 9 4 $ # " 1 4 & % 1/ 4 A. 3 / 4 B. 4 / 3 C. - 3 / 4 D. - 4 / Simplify the expression. ( 4 ) 1/ 4 A. 4!!! B. C. 4 /4 D. None of the above