Algebra IA Final Review

Transcription

1 Algebra IA Final Review Name: 1. Bob knows there is a relationship between how much time he spends chatting with his classmates and how many problems he can get done in Algebra class. Identify the Independent Quantity and the Dependent Quantity in this problem situation. Sketch a graph of the scenario and label the quantities and units. Independent Quantity: Dependent Quantity:. Tell whether each graph represents a function. a. c. b. d.

2 3. Identify the function family of a graph that is made up of an increasing or decreasing curve, has no absolute maximum or absolute minimum, and doesn t have symmetry. 4. Classify each function as increasing, decreasing, or constant. a. f(x) = -10 b. f(x) = -4x + 5. Classify each function as a linear function, a linear absolute value function, a quadratic function, or an exponential function. a. f(x) = 3x c. f(x) = x b. f(x) = x - 10 d. f(x) = x² Determine whether each function has an absolute maximum or absolute minimum. If the graph has neither an absolute maximum nor an absolute minimum, write none. a. f(x) = 5 b. f(x) = - x Evaluate the functions. Let and. a. f() b. f(-3) c. g(5) d. g(-1)

3 8. Determine what function family the graphs belong to. (constant, linear, quadratic, absolute value, or exponential) a. b. c. d. 9. Indicate which graphs have the following characteristics: Increasing, decreasing, Absolute Maximum, Absolute Minimum. a. b. c. d. 10. Sketch a graph with the given characteristics. is quadratic, is discrete, has a Maximum, and is a function.

4 11. Sketch a graph with the given characteristics. is a function is an Absolute Value is continuous has an absolute maximum 1. Complete the table of values and sketch the graph. x f(x) = x² - 1 (x, f(x)) y x Which is a linear function? a. f(x) = - x b. f(x) = -x c. f(x) = -x + d. f(x) =-x² 14. What is the classification of the function f(x) = x² - 50? a. linear absolute value function b. exponential function c. quadratic function d. linear function

5 15. Which best describes the behavior of the function f(x) =? a. It is constant. b. It is increasing. c. It is decreasing. d. It is both increasing and decreasing. 16. Which equation does not represent a function? a. x = 5 b. y = - 8x + 3 c. y = 4x - 1 d. y = x² Which statement about the function f(x) = x + 5 is true? a. It has an absolute minimum. b. It has an absolute maximum. c. It has both an absolute minimum and an absolute maximum. d. It has neither an absolute minimum nor an absolute maximum. 18. Which is a quadratic function? a. f(x) = - x + 9 b. f(x) = -8 x c. f(x) = x² + 4 d. f(x) = -x + 3 Solve each equation. Clearly show all steps. Circle final answer. x x (x + 4) = x 11x 9 = x 10 = -3x (4x ) = -14 1x

6 5. Alfred works as an assistant manager at Old Navy. The table shows his pay after various times. Units Time Pay Hours $ Expression t a. What are the dependent and independent quantities (and units) in this problem situation? b. Determine the unit rate of change for the problem situation. c. Complete the table. Write an expression that represents the pay for an arbitrary time t hours in the last row. d. Use function notation to determine his pay for 35 hours. Show your work. e. How many hours does Alfred work to earn $500? Show your work.

7 6. Jules is raising money for club by selling cornucopia centerpieces (x) for $1 each. He has already raising $95 from a previous fund raiser. How many centerpieces does he have to sell to reach his goal of $450. Write an inequality and solve. Solve each inequality, and graph the solution on the number line. m v > (3y 4) m < Solve each absolute value equation. Show all steps. 30. x x x x 5 0

8 34. A number is greater than 14 and less than. Write a compound inequality that represents the possible values of the number. Then graph the compound inequality on the number line. 35. Represent the solution to each compound inequality on the number line shown. Then, write the final solution that represents the graph. a. b x 5 < Or

9 38. And 39. What is the value of the linear absolute value expression: 40. What is the solution to the inequality:? 41. What is the value of the linear absolute value expression:? 4. Which compound inequality has no solution? a. b. c. d. 43. Use the literal equation to convert between Fahrenheit and Celsius. Show your work. a. 51 C b. 3 F

10 44. Holly has $00 to spend at the shopping mall. She decides to buy sweaters and pants with her money. Sweaters cost $30 each and pants cost $5 each. a. Write an equation to represent this problem situation. Use s to represent the number of sweaters and p to represent the number of pants. b. If Holly buys 3 sweaters, what is the greatest number of pants she can buy? Show your work and explain your reasoning. c. If Holly buys no pants, what is the greatest number of sweaters she can buy? Show your work and explain your reasoning. 45. Determine the x-intercept and y-intercept of each equation. a. 0x + 8y = 30 b. y = -13x Graph each equation using the x- and y-intercepts. a) -x - y = 6 b) 10x 0y = 60 x-intercept: y-intercept: x-intercept: y-intercept: y y x x 4 6

11 47. Solve the formula for b. Show your work. 48. Write the equation in standard form. a. b. 49. Write the equation in slope-intercept form. a. b. 50. Determine the next three terms in the sequence. Write an explanation for the pattern. a. -1, -18, -15, -1, b. 81, 64, 49, 36, c..3, 4.6, 9., 18.4, 51. Identify each sequence as arithmetic or geometric. Then determine the common difference or common ratio for each sequence. a. 13, 9, 5, 1, -3, b. 96, 48, 4, 1, 6, 5. Write the first 4 terms of each sequence: a. An arithmetic sequence with a common difference of -3 and a first term of -1. b. A geometric sequence with a common ratio of 3 and a first term of -5.