Name Date Class Unit 4 Test 1 Review: Linear Functions

Transcription

1 Name Date Class Unit 4 Test 1 Review: Linear Functions Select the best answer. 1. Does this graph represent a linear function? Explain your answer in the space provided. 2. A jogger runs 4 mi/h. The function f(x) = 4x gives the distance the jogger travels in x hours. Graph this function. Give its domain and range. domain: range: 3. This table shows the number of people at a festival at certain times during the day. (A) During which time interval did the number of people increase at the greatest rate? (B) What was the rate of change for that interval? Hour (PM) Number of People

2 Name Date Class 4. State whether the slope of this line is positive, negative, zero, or undefined. 5. Find the slope of the line that contains the points (4, 5) and (7, 11). 6. State whether this relationship is a direct variation. Explain your answer in the space provided. x y Francis leaves home and goes to the store for her mother. On the way, she stops and talks with her friend, Angela. She then continues to the store and finally returns home. The graph at the right depicts her distance from home as time elapses. (A) Determine the rate of change between points C and D. (B) What event occurs at point A? (C) What event occurs at point E? (D) What is different about the rate of change between points B and C compared to the other rates of change on the graph?

3 8. Use the table to answer the following questions. (A) Is the rate of change for the function represented by the table a constant rate? (B) If yes, what is the constant rate? If no, explain why there is not a constant rate. Input (x) Output f(x) Use the table to answer the following questions. (A) Is the rate of change for the function represented by the table a constant rate? (B) If yes, what is the constant rate? If no, explain why there is not a constant rate. Domain Range Find the slope for the following ordered pairs: (A) (-2, 0) (5, 7) (C) (1, 4) (1, -3) (B) (9, 3) (-2, 3) (D) (8, -5) (3, -2) 11. State whether the slopes are positive, negative, zero, or undefined. (A) (B) (C) (D) 12. Find the slope of the given line.

4 13. Grandma is driving a car that moves at a velocity of 50mph while traveling from Greenville to Jacksonville a total distance of 300 miles. (A) Fill in the missing values on the table below. Hours Distance (B) Use the table to complete the graph. (Label axes) (C) What would the rate of change be for this function? Select the best answer. 14. In the equation y = -6x, if the value of x is decreased by two, what is the effect on the value of y? (A) It is increased by six (C) It is increased by twelve (E)It is twelve times the original amount (B) It is decreased by twelve (D) It is two times the original amount 15. Yvonne has studied the cost of tickets over time for her favorite sports team. She has created a model to predict the cost of a ticket in the future. Let C represent the cost of a ticket in dollars and t represent the number of years in the future. Her model is as follows. C = 4.00t + 12 Based on this model, how much will the cost of a ticket increase in two years? (A) $8 (B) $16 (C) $20 (D) $12 (E) $ Carla has a lemonade stand. Her profit is modeled by y = 0.25x 6.00 where y is profit and x is the number of cups of lemonade sold. If she sells five cups of lemonade, how much money does she make today?

5 17. Which graph represents a linear function? (A) (B) 18. A car travels at 60 mi/h. The function f(x) = 60x gives the distance the car travels in x hours. What is the range of this function? (A) y 0 (B) {0, 1, 2, 3,...} (C) {0, 60, 120, 180,...} (D) all real numbers 19. The volume V of gas varies directly to the pressure P. If the volume of a gas is 220 cm 3 under pressure of 20 kg/cm 2, what will happen to its volume under pressure of 36 kg/cm 2? 20. If x varies directly as y, and x = 12 when y = 8, find x when y is 4. (A) 42 (B) 16 (C) 31 (D) 27 (E) 6 21.Classify the following example as Direct or Inverse Variation: A car is traveling a constant speed of 65 mph the distance the car travels is related to the time by the equation D = 65t, where t is in hours. (A) Direct (B) Inverse (C) Neither 22. Classify the following graph as Direct or Inverse Variation: (A) Direct (B) Inverse (C) Neither 23. Which is a direct variation equation that has the ordered pair (-1, 8) as a solution? (A) y = 8x + 7 (B) y = -8x + 10 (C) y = -8x (D) y = 8x 24. Identify the constant of variation in the equation y = -12x.

6 25. What point on the coordinate plane does a direct variation always pass through? 26. In a direct variation, if the x coordinates are decreasing what will happen to the y coordinates? 27. Determine the rate of change for each segment below: The table shows the price of a video game for different years since the game was released. During which time interval did the price decrease at the greatest rate? Year Price ($) (A) 2000 to 2002 (B) 2003 to 2005 (C) 2002 to 2003 (D) 2005 to Find the slope of the line that contains the points (6, 8) and (2, 1). (A) 7 4 (B) 9 8

7 31. The slope of this line is. (A) positive (B) zero (C) negative (D) undefined 32. Is this relationship a direct variation? X Y (A) yes (B) no 33. Which set of ordered pairs satisfies a linear function? (A) (C) x x y y (B) x (D) x y y A vacation home in Orlando, Florida, rents for $105 per day. The function f(x) = 105x gives the cost of renting the home for x days. What is the domain of this function? (F) x 0 (G) {0, 1, 2, 3,...} (H) {0, 105, 210, 315,...} (J) all real numbers 35. A parking meter gives 30 minutes for each quarter and 6 minutes for each nickel. The equation 30x + 6y = 60 describes the number of quarters x and nickels y that you need to park for 60 minutes. What does the x-intercept represent? (A)You need 2 quarters and no nickels to park for 60 minutes. (B)You need 10 nickels and no quarters to park for 60 minutes. (C)You need 6 nickels and no quarters to park for 60 minutes. (D)You need 30 quarters and no nickels to park for 60 minutes. 36. Which equation is NOT a direct variation? (A) y = 50x (B) -2y = x (C) 5x + 2y = 10 (D)-3x + 2y = 0

8 37. This table shows the U.S. federal minimum hourly wage in different years. During which time interval did the wage increase at the greatest rate? Year Wage ($) (F) 1979 to 1980 (G) 1981 to 1990 (H) 1980 to 1981 (J) 1990 to Find the slope of this line. (A) (B) 2 5 (C) (D) 5 2 Use the graph to answer questions 39 and What was Hosni's rate of change in the 1 st 3 seconds? 40. What was Hosni's rate of change from 6 sec to 10 sec?

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