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ALGEBRA 1 EOC REVIEW 1 PART 2 (LINEAR FUNCTIONS)

ALGEBRA 1 EOC REVIEW 1 PART 2 (LINEAR FUNCTIONS). 1). Suppose that the function: f(x) = 3 x + 14 represents the cost to rent x video games from a local store. Jack has $ 19 in his wallet. How much more will he need in order to rent 5 video games this month?. f(x) = 3(5) + 14.

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ALGEBRA 1 EOC REVIEW 1 PART 2 (LINEAR FUNCTIONS)

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  1. ALGEBRA 1 EOC REVIEW 1 PART 2 (LINEAR FUNCTIONS)

  2. 1) Suppose that the function: f(x) = 3 x + 14 represents the cost to rent x video games from a local store. Jack has $ 19 in his wallet. How much more will he need in order to rent 5 video games this month? f(x) = 3(5) + 14 money needed: $ 29 – $ 19 = $ 10 f(x) = 15 + 14 f(x) = 29

  3. 2) A bag of lollipops contains 20 lollipops. Each lollipop costs $ .10. How much will a club have to sell each lollipop to make a profit of $ 5 per box? 20 x – 2 = 5 20 x = 7 x = $ .35

  4. 3) Cell Phone company A charges $ 20 per month plus $ 0.10 per text. Cell Phone B charges $ 25 per month with no charge per text. Write the function that represents: A: f(x) = .1 x + 20 a) Each plan B: g(x) = 25 b) The combined costs of the two plans. f(x) + g(x) = .1 x + 45 c) The difference in cost between A and B. f(x) – g(x) = .1 x – 5

  5. 4) Find the slope, y-intercept, and x-intercept of the following. Then circle the highest slope, highest y-intercept, and the largest x-intercept. a) The line going between (2, 3) and (4, 5). - 1 y-intercept 1 x-intercept Slope: 1 b) x-intercept of 3; y-intercept of - 4 y-intercept x-intercept Slope: - 4 4/3 3 c) 2 Slope: 6 y-intercept 3 x-intercept

  6. 5) The exchange rate (including a transfer fee) from Japanese Yen to US Dollar is D = .0097 Y + 4 where D is dollar and Y is Yen. (multiple choice) a) The amount of dollars increases by 4 per yen. b) The amount of dollars increases by .0097 per 100 yen. c) The amount of dollars increases by 40 per 100 Yen. d) The amount of dollars increases by .97 per 100 yen.

  7. 6) The equation for Jack’s savings is f(x) = 8 x + 20 and for Paul’s savings is g(x) = 4 x + 3 where x is the number of weeks. a) How much is Jack’s savings per week? $ 8 b) How much did Paul have in his account initially? $ 3 c) What is the meaning of f(x) = g(x)? Find it algebraically and by graphing both equations. When their savings will be the same. 8 x + 20 = 4 x + 3 Savings will never be the same. Cannot have a negative number of weeks. 4 x = - 17 x = - 4.25

  8. 7) There were originally 4000 trees in the forest. Each year, a certain number of trees were cut down. After 15 years, there were 1900 trees. Find the equation that determines how many trees there are per year. (15, 1900) (0, 4000) y = - 140 x + 4000

  9. 8) The surface area of a sphere is 500 cm2. What is the approximate diameter of the sphere? (SA = 4 п r2) 4 п r2 = 500 r = 6.31 d = 2 r = 2(6.31) = 12.62

  10. 9) F(x) = 3 x + 2. g(x) is defined by the line that goes through (5, 6) and (7, 8). 6 = 1(5) + b g(x) = x + 1 6 = 5 + b 1 = b a) Find the difference of their slopes. 3 – 1 = 2 b) Find the difference of their y-intercepts. 2 – 1 = 1

  11. 2) Solve the equation: 2 x – 3 – 7 x = 10 – 4 x + 6 - 5 x – 3 = - 4 x + 16 - x – 3 = 16 - x = 19 x = - 19

  12. 3) Solve each equation for the specified value: a) 5 a b – 3 b c = 10 for c - 3 b c = - 5 a b + 10 b) a – b = 3 d(b – c) a – b = 3 b d – 3 c a = 3 b d – 3 c d + b

  13. 4) • Find the value of a, knowing that b = - 1, • c = 5, and d = - 3 - 15 = a + 2 - 17 = a • Find the value of b, knowing that a = 3, • c = - 2, and d = 1. 5/2 = b = 2.5 - 2 = 3 – 2 b - 5 = – 2 b c) Find the value of c, knowing that a = - 6, b = 4, and d = - 5. - 5 c = - 14 c = 14/5 = 2.8

  14. 4) d) Solve the formula for “a”. d c = a – 2 b d c + 2 b = a e) Solve the formula for “b”. d c = a – 2 b d c – a = – 2 b f) Solve the formula for “c”. d c = a – 2 b

  15. 1) Find the x and y intercepts of the following functions: a) f(x) = 2 x – 4 - 4 x-intercept: y-intercept: 2 b) f(x) = x2 + 2 x – 3 x-intercept: y-intercept: - 3 {- 3, 1} c) f(x) = 3 • e2x x-intercept: y-intercept: none 3

  16. Given the graph below: 2) • What are the x-intercepts of the function f? • What is the y-intercept? x-intercepts: y-intercept: - 2 {- 13, 2, 9}

  17. Given the graph below: 2) b) Can a function have more than one y-intercept? Explain your answer. No, points on the graph of a function cannot have the same x-coorinates.

  18. Given the graph below: 2) c) Where is the function f increasing? Decreasing? Increasing: Decreasing: • 6 ≤ x ≤ 6 and • x ≥ 6 - 6 ≤ x ≤ 6

  19. Given the graph below: 2) d) Where is the function f positive? Negative? Positive: Negative: - 113 ≤ x ≤ 0 and x ≥ 9 2 ≤ x ≤ 6 and x ≤ - 13

  20. Given the graph below: 2) e) Where are the relative minimums and maximums of the function f? Relative Minimums: Relative Maximums: (6, 5) (- 6, - 6)

  21. Given the graph below: 2) f) Is there any symmetry? Explain your answer.

  22. Ione has no more than $ 80 to buy tickets to a football game for her friends and family. Student tickets cost $ 3 and non-student tickets cost $ 5 each. Ione graphed 3 x + 5 y ≤ 80 to determine how many of each kind of ticket she can buy. Which describes the point (5,13)? 20) A) Ione has $ 5 left after buying 13 non-student tickets. B) Ione has $ 13 left after she buys 5 student tickets. C) Ione can buy 5 non-student tickets and 13 student tickets. D) Ione can buy 5 student tickets and 13 non-student tickets.

  23. Which best describes the domain and range of the function y = 5 x – 3? 3) A) domain: all real numbers; range: all real numbers B) domain: positive real numbers; range: all real numbers greater than 2 C) domain: nonnegative real numbers; range: positive real numbers D) domain: all real numbers; range: real numbers greater than 3/5

  24. Carl has budgeted $ 60 to buy pork ribs and chicken legs for a faculty barbeque. Ribs cost $ 3.75 per pound, and chicken legs cost $ 3.00 per pound. If Carl buys x pounds of chicken, which best represents the number of pounds y of ribs he can buy and not exceed his budget? 6) A) y ≤ - 3 x + 60 B) y ≤ - 0.8 x + 16 C) 3.75 y – 60 ≤ 3 x D) 3 x + 3.75 y ≥ 60

  25. A Raleigh company has monthly expenses represented by the function C(x) = 16 x + 4,200, where x represents the number of items produced. For how many items produced is the monthly cost $ 81,000? 8) A) 1,300,200 B) 5,325 C) 5,063 D) 4,800 16 x + 4200 = 81000 16 x = 76800 x = 4800

  26. 13) An Internet wholesaler charges vendors $ 5.10 for each bottle of herbal hand lotion plus $ 27.50 per order for shipping. What is the total cost to a vendor for ordering 72 bottles of the hand lotion? A) $ 367.20 B) $ 387.50 C) $ 394.70 D) $ 2, 347.20 y = (5.1)(72) + 27.5 y = 394.70

  27. 14) A company that manufactures and sells surfboards uses the function P = 40 s – 200,000 to estimate its profit P on the sale of surfboards. How many boards must the company sell to make $ 1,200,000 in profit? A) 35,000 B) 45,000 C) 350,000 D) 450,000 40 s – 200000 = 1,200,000 40 s = 1,400,000 s = 35,000

  28. 15) Which is the graph of the solution set of 2 x + y ≥ 3? y ≥ - 2 x + y B) A) D) C)

  29. SOLVING EQUATIONS: 1) 3 x + 2 = 8 3 x = 6 x = 2

  30. SOLVING EQUATIONS: 2) 5(3 – x) + 4 = 22 15 – 5 x + 4 = 22 – 5 x + 19 = 22 – 5 x = 3 x = - 3/5 = - .6

  31. SOLVING EQUATIONS: 3) 3(2 x + 5) = 5(9) 6 x + 15 = 45 6 x = 30 x = 5

  32. SOLVING EQUATIONS: 4) 7 – x = 3 x – 5 7 – 4 x = - 5 – 4 x = - 12 x = 3

  33. SOLVING EQUATIONS: 5) 3(2 x + 5) = 4 x – 2 6 x + 15 = 4 x – 2 2 x + 15 = – 2 2 x = – 17 x = – 17/2 = - 8.5

  34. Solve for t: 6) 6 t + 3 r = 2 t – 4 4 t + 3 r = - 4 4 t = - 3 r – 4

  35. Solve for y: 6) y – 3 x = 2 a y = 2 a + 3 x

  36. SOLVE THE INEQUALITY: 1) 2 x + 2 < 8 2 x < 6 x < 3

  37. SOLVE THE INEQUALITY: 2) - 3 ≤ 3 – 6 x - 6 ≤ - 6 x - 6 x ≥ - 6 x ≤ 1

  38. SOLVE THE INEQUALITY: 4) 8 + t < 3 t – 5 8 – 2 t < - 5 – 2 t < - 13 t > 13/2 = 6.5

  39. SOLVE THE INEQUALITY: 5) 3(2 x + 5) ≤ 2(9) 6 x + 15 ≤ 18 6 x ≤ 3 x ≤ 3/6 = ½ = .5

  40. 6) Michael weights 250 pounds. He wants to weigh less than 215 pounds. If he can lose an average of 2.5 pounds per week on a certain diet, how long should he stay on his diet to reach his goal? 250 – 2.5 x ≤ 215 – 2.5 x ≤ - 35 x ≥ 14 He must diet for at least 14 weeks.

  41. 7) Jeffrey wants to gain muscle for the football season and can gain 1.2 pounds each week. If he currently weighs 190 pounds and wants to weigh more than 211, how many weeks will it take to reach his goal? 1.2 x + 190 ≥ 211 1.2 x ≥ 21 x ≥ 17.5 It will take at least 17.5 weeks.

  42. 8) Sarah scores on 4 health tests are 75, 83, 78, 89. The fifth and final test of the grading period is tomorrow. She needs to average (mean) at 85 on all her tests to receive a C for the grading period. a) If s is her score on the fifth test, write an inequality to represent the situation. b) If Sarah wants a C in the class, what score must she score on the test? 325 + s = 425 s = 100

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