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Unit 1 Post-Test Modeling Functions NAME: ______________________________ DATE: ________ Period : ______ REVIEW SHEET SCORE: Solve a system of equations Solve a system of inequalities Solve for a specific variable Graph linear, absolute value, and quadratic functions Write linear, absolute value, and quadratic functions Evaluate and apply various functions ALGEBRA: ______ / _______ = _______% FUNCTIONS: ______ / _______ = _______% ALGEBRA 1. Two brothers are saving money to buy tickets to a concert. Their combined savings is $75. One brother has $35 more than the other. How much has each saved? X + y = 75, x + 35 = y; x + (x + 35) = y; x = 20, y = 35 2. Solve for h: V r 2h v/∏r2 = h 3. Last year the volleyball team paid $5 per pair of socks and $17 per pair of shorts on a total purchase of $315. This year they spent $342 to buy the same number of socks and shorts because the socks now cost $6 and the shorts now cost $18. How many pair of socks and shorts did the team buy each year? 5x + 17y = 315, 6x + 18y = 342; x = 15, y = 14 4. Solve the system: 2x – y = 2 2x – 2 y = 4 (0, -2) 5. Your candy factory is making chocolate-covered peanuts and chocolate-covered pretzels. For each case of peanuts, you make $40 profit. For each case of pretzels you make $55 profit. The table below shows your conditions. Production Hours Peanuts Pretzels Maximum Hours Machine Hours 2 6 150 Man Hours 5 4 155 a. Write a system of inequalities to represent the situation. b. Graph the system of inequalities and Label your vertices. c. How many cases of each product should you make to maximize profit? What is the profit you will make? ________ peanuts ________ pretzels Profit: _______________ FUNCTIONS Voting in Presidential Election Years The table shows the percent of people of voting age who reported they voted in presidential election years. Year % who voted 1988 57 1992 61 1996 54 2000 55 2004 58 SOURCE: HTTP://WWW.CENSUS.GOV/POPULATION/WWW/SOCDEMO/VOTING.HTML#HIST 6. Represent the data using each of the following: a. a mapping diagram 1988 54 1992 55 1996 57 2000 58 2004 61 b. ordered pairs c. graph on coordinate plane (1988, 57), (1992, 61), (1996, 54), (2000, 55), (2004, 58) 7. Write a function to model the cost of renting a truck for one day. Then evaluate the function for the given number of miles. Daily rental: $39.95 Rate per mile: $.60 per mile Miles traveled: 48 miles 8. Evaluate the function for the given value of x, and write the input x and the output f (x) as an ordered pair. a. f(x) = ½ x – 1 for x = -2 f(-2) = -2 b. Find the Error: Evaluate f(x) = 3x2 – 4x + 1 for x = -5 f( -5) = 3(-5)2 – 4(-5) + 1 f( -5) = 3(10) – 4(-5) + 1 f( -5) = 51 9. Given (2, -3) and (-4, -5) find the following: a. Calculate the slope between the points b. Write the equation of the line passing through those points c. Write the equation of the line parallel to the one you found in part (b) passing through (6, 1) d. Write the equation of the line perpendicular to the one you found in part (b) passing through (6, 1) e. Graph the equation of the line you found in part (b). 10. A company in Greensboro manufactures piston rings that are to be 5.25 inches in diameter. A ring is rejected if its diameter, d, is off by more than 0.0125 inch. a. Write an absolute value inequality that represents this situation. |d – 5.25| ≤ .0125 b. Solve. State the meaning of the answer in the context of the problem. The diameter can be between 5.2625 and 5.2375 11. Write the function represented in each graph. Then state the domain and range of each. a. b. y = 2(x + 1)2 – 4 Y < 1/3x + 1 c. y = 4|x| + 1/2 12. Use the function, f ( x) 2 x 1 3 answer the following: a. Graph the function (label the vertex) Vertex: (1, 3) b. State the transformations to the parent graph Right 1, Up 3, Stretched by factor of 2 c. State the domain and range of the function D = All real numbers; R = All real numbers greater than or equal to 3 1 3 13. Use the function, f ( x) x 2 4 x 16 answer the following: a. Graph the function (label the vertex, axis of symmetry, and y-intercept) A of S: x = -6; Vertex: (-6, -4); y-intercept = -16 b. Write the function in vertex form y = -1/3(x + 6)2 – 4 c. State the transformations to the parent graph Left 6, down 4, compressed by factor of 1/3, reflected across the x-axis d. State the domain and range of the function. D = all real numbers; R = All real #’s ≤ -4 14. A player hits a tennis ball across the court and records the height of the ball at different times, as shown in the table. Time(s) Height (ft) a. Find a quadratic model for the data. -1/2x2 + x + 5.5 0 5.5 1 6.0 b. Use the model to estimate the height of the ball at 4 seconds. 1.5 feet 2 5.5 c. What is the ball’s maximum height? 6 ft 3 4.0 15. A small independent motion picture company determines the profit P for producing n DVD copies of a recent release is P = 0.02n2 + 3.40n 16. P is the profit in thousands of dollars and n is in thousands of units. a. How many DVDs should the company produce to maximize the profit? 85 thousand DVDs b. What will the maximize profit be? $128,500 Performance Tasks: ALGEBRA 16. Given the inequality │x + 2│ ≤ k , find a value of k, if possible, that satisfies each condition. In each case, explain your choice. a. Find a value of k such that the inequality has no solution. b. Find a value of k such that the inequality has exactly one solution. c. Find a value of k (different from your value in part b) for which a solution exists but for which the solution set does NOT include 5. FUNCTIONS 17. Write a short paragraph about the similarities and differences of the types of functions covered in this unit (linear, absolute value, quadratic). Reference which functions are even and which are odd and justify your choice. Be sure to thoroughly answer in vivid detail. (BONUS) Given the data below: Find the recursive and explicit equations: