Unit III Practice Questions

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1 Unit III Practice Questions 1. Write the ordered pair corresponding to each point plotted below. A F B E D C 2. Determine if the ordered pair ( 1, 2) is a solution of 2x + y = 4. Explain how you know. 3. Determine if the ordered pair ( 1, 3) is a solution of 3x + y = 6. (Show work.) Explain how you know. 4. Graph the equation y = 3x + 4 by plotting at least three points. 5. Graph the equation y = 1 x by plotting at least three points Graph the equation y = 2x 5 by plotting at least three points. 7. Graph the equation x + 4y = 8 by plotting at least three points. 8. For the ordered pair (x, 3), find the value of x that satisfies the equation 3x + 2y = For the ordered pair (2, y), find the value of y that satisfies the equation 3x 2y = What point could be an x-intercept for a graph? ( 1,1) ( 3, 3) ( 0, 4) ( 1 2, 0 ) 11. What point could be a y-intercept for a graph? ( 2, 3) ( 0, 3) 3 2, 2 3, 0 3 ( ) 12. Which equation is a vertical line? 2x + 3y = 1 y = 0 x = 4y 1 x = Which equation is a horizontal line? x = x y = 7 y = 2x 2 y = 0

2 14. (a) Find the x-intercept and the y-intercept of the equation 3x 4y = 12, and write each as an ordered pair. (b) Plot the intercepts and draw a graph of the line. 15. (a) Find the x-intercept and the y-intercept of the equation 9x 3y = 18, and write each as an ordered pair. (b) Plot the intercepts and draw a graph of the line. 16. Graph the equation x = Graph the equation y = Graph the equation y = x. 19. Find the slope of the line through the points (6, 0) and ( 2, 3). 20. Find the slope of the line through the points (8, 2) and ( 2, 5). 21. Find the slope of the line y = 3x Find the slope of the line 4 y = 1 5 x. 23. Find the slope of the line y = Find the slope of the line x = The cost, C, of renting a YOU-HAUL truck is $29 plus $0.50 per mile, m. (a) Write an equation for the cost of the truck using m for the number of miles driven. (b) Graph the equation for up to 200 miles. (c) Find the cost of a 125-mile trip. (d) Find the length of a trip that costs $ The cost, c, of subscribing to digital cable involves an installation fee of $79, plus a $35 monthly programming fee, p. (a) Write an equation for the cost of cable using p for the number of months. (b) Graph the equation for up to 24 months. (c) Find the cost of having digital cable for a year. (d) How long has Bob had cable if he has paid a total of $639? 27. Write an equation in slope-intercept form for the line with slope = 3 4 and y-intercept = 1.

3 28. Choose the description that fits the given line. A. slope is positive, y-intercept is positive B. slope is positive, y-intercept is negative C. slope is negative, y-intercept is positive D. slope is negative, y-intercept is negative 29. Choose the description that fits the given line. A. slope is positive, y-intercept is positive B. slope is positive, y-intercept is negative C. slope is negative, y-intercept is positive D. slope is negative, y-intercept is negative 30. Choose the description that fits the given line. A. slope is zero, y-intercept is positive B. slope is zero, x-intercept is positive C. slope is undefined, y-intercept is positive D. slope is undefined, x-intercept is positive 31. Choose the description that fits the given line. A. slope is zero, y-intercept is positive B. slope is zero, x-intercept is positive C. slope is undefined, y-intercept is positive D. slope is undefined, x-intercept is positive

4 32. (a) Find the slope of the line graphed here. (b) Find the y-intercept of the line. (c) Write an equation for the line. 33. (a) Find the slope of the line graphed here. (b) Find the x-intercept of the line. (c) Write an equation for the line. 34. (a) Find the slope of the line graphed here. (b) Find the y-intercept of the line. (c) Find the x-intercept of the line. (d) Write an equation for the line. 35. Write an equation in slope-intercept form for the line with slope = 1 3 and y-intercept: (0, 4). 36. Find the slope and y-intercept of the line 3x 2y = 4 and use these to draw the graph. 37. Find the slope and y-intercept of the line 4x + 2y = 6 and use these to draw the graph. 38. Use the slope and y-intercept to graph the line y = 4x Find an equation in slope-intercept form of the line through the points (0, 5) and ( 2, 3).

5 40. Find an equation in slope-intercept form of the line through the points (0, 4) and (2, 6). 41. Are the following lines parallel (yes or no, and why)? 7x + 3y = 12 y = 7 3 x Find the pair of parallel lines: (a) 2x + 3y = 9 (b) y = 2x 9 (c) 3x 2y = 6 (d) y = 3 2 x Find the pair of parallel lines: (a) 2x 3y = 10 (b) 3x + 2y = 12 (c) y = 2 3 x + 4 (d) y = 3x Write an equation in slope-intercept form of the line through the point (0, 1) and parallel to the line y = 4x Evaluate the function at the indicated value. f (x) = x 2 5x 4; find f ( 3). 46. Express the relation as a set of ordered pairs. Then write the domain and range. Also tell whether or not the relation represents a function and why or why not. x y Express the relation as a set of ordered pairs. Then write the domain and range. Also tell whether or not the relation represents a function and why or why not. x y Evaluate the function at the indicated value. f (x) = x 2 3x 5; find f ( 2). 49. Determine whether the following graph represents a function. Tell why or why not.

6 50. Determine whether the following graph represents a function. Tell why or why not. 51. Determine whether the following graph represents a function and tell why or why not. Also state the domain & range. 52. The monthly profit of a small business is given by the function P(x) = 4x 1600, where x represents the number of items sold. (a) What is the profit from selling 1200 items? (b) If the profit is $2000, how many items were sold? 53. The weekly cost for a small business is given by the function C(x) = 2x + 900, where x represents the number of items sold. (a) What is the cost when selling 1200 items? (b) If the cost is $2000, how many items were sold? 54. (True/False) If a relation has two ordered pairs with different x-values but the same y-values, than the relation cannot be a function.

7 55. Stacy Best owns a weight loss clinic. She charges her clients a one-time membership fee. She also charges per pound of weight lost. Therefore, the more successful she is at helping clients lose weight, the more income she will receive. The following graph shows a client s cost for losing weight. Use the graph to answer the questions. $ weight loss (a) Estimate (from the graph) the initial membership fee. (b) Estimate the cost for a client who loses 40 pounds. (c) If a client was charged $150, how much weight did he lose? 56. Graph the function: f (x) = 1 2 x Graph the inequality: y > 2x Graph the inequality: 3x + 4y Graph the inequality: x < Graph the Inequality: y Solve each of the following systems by the substitution method. x + 3y = 28 3x 2y =19 a. b. y = 5x x + y = 8

8 62. Solve each of the following systems by the addition(elimination) method. x + y =10 5x = y + 5 a. b. x y = 6 5x + 2y = Solve each of the following systems by the addition(elimination) method. x + y = 3 4x 3y = 19 a. b. 3x + 2y = 19 3x + 2y = Steve Watnik wishes to mix coffee worth $6 per lb. with coffee worth $3 per lb. to get 90 lbs. of a mixture worth $4 per lb. How many pounds of the $6 and $3 coffees will be needed? 65. A 40% dye solution is to be mixed with a 70% dye solution to get 120 L of a 50% solution. How many liters of the 40% and 70% solutions will be needed? 66. Graph the solution to the system of inequalities: x 5 y 3 2x + 3y < Graph the solution to the system of inequalities: x y < 5

9 ANSWERS for Unit #3 Practice Questions 1. A ( 5, 4) B (1, 3) C (4, 0) D (2, 5) E ( 2, 5) F (0, 1) 2. Yes. True statement when ( 1, 2) is substituted into equation. 3. No. False statement when ( 1, 3) is substituted into equation x = y = ( 1 2, 0 ) 11. (0, 3) 12. x = y = (a) x-int (4, 0); y-int (0, 3) 5. (b) (a) x-int (2, 0); y-int (0, 6) (b)

10 (a) c = p (b) $1000 $600 $ (c) $499 (d) 16 months y = 3 4 x C 29. B 30. A 31. D 32. (a) m = 0; (b) (0, 3); (c) y = m = m = (a) m undefined; (b) ( 4, 0); (c) x = (a) m = 1 ; 2 (b) (0, 2); (c) (4, 0); (d) y = 1 2 x m = y = 1 3 x m = m = m = 3 ; y-int (0, 2) 2

11 24. m is undefined 25. (a) C = m (b) $125 $75 $ (c) $91.50 (d) 96 miles 37. m = 2; y-int (0, 3) 48. f ( 2) = Not a function; fails vertical line test points 50. function; no vertical line hits two 51. function; passes vertical line test 38. m = 4 ; y-int (0, 2) 52. (a) P(1200) = $3200 (b) 900 items 53. (a) C(1200) = $3200 (b) 550 items 54. False 55. (a) about $100 (b) about $200 (c) about 20 lbs. 39. y = x y = x No 42. c & d 43. a & c 44. y = 4x f ( 3) = 20

12 46. {(-1, 4), (-5,-2), (-3, 0), (4,-3), (6, 4)} DOM = {-1, -5, -3, 4, 6} 57. RNG = {4, -2, 0, -3, 4} function, since no x is paired with two y s 47. {(-1, -4), (5, -2), (3, 0), (4, 3), (5, 4)} DOM = {-1, 5, 3, 4} RNG = {-4, -2, 0, 3, 4} not a function, since 5 is paired with 2 & y y x 59. x y 60. x

13 61. a. x = 2; y = 10 b. x = 7; y = a. x = 2; y = 8 b. x = 2; y = a. x = 5; y = 2 b. x = 2; y = lb. of $6 and 60 lb. of $ L of 40% solution and 40 L of 70% solution y x

Linear Equations. Find the domain and the range of the following set. {(4,5), (7,8), (-1,3), (3,3), (2,-3)}

Linear Equations. Find the domain and the range of the following set. {(4,5), (7,8), (-1,3), (3,3), (2,-3)} Linear Equations Domain and Range Domain refers to the set of possible values of the x-component of a point in the form (x,y). Range refers to the set of possible values of the y-component of a point in