Unit 2 Practice Test Algebra II READ THIS: You asked for more problems, so I gave them to you. Remember that you don’t have to complete every problem. Spend your time working on those that you need practice with. Important Questions: When is the test? When does Mr. Clithero stay after school? Can use Desmos on the test? Can you use a graphing calculator? What is a function? How do you determine if a function is linear from the graph, the rule, or the table? What do the graphs of each parent function look like? What is modeling? Transformation Horizontal Vertical Fill in the table. Reflection (flip) Translation (slide) Stretch or shrink For two-variable inequality graphs, what does the shading represent? Vocab: equation, relation, function, input, output, domain, range, linear, slope, y-intercept, slopeintercept from, point-slope form, parallel, perpendicular, direct variation, linear modeling, quadratic, cubic, square root, absolute value, exponential, rational, transformation, translation (slide), reflection (flip), stretch, shrink, inequality, include, exclude, solution Review Questions: 2.1 Relations and Functions 1. What is the Vertical Line Test? 2. Give an example of a relation that is not a function for a table, graph and mapping diagram. 3. Give an example of a function for a table, graph and mapping diagram. 4. Give the domain and range for one of the tables below. 5. Give the domain and range for the quadratic parent function. 6. Give the domain and range for cubic parent function. 7. Give the domain and range for the square root parent function. 8. Find the rule (the last row is hard) x y x f(x) x y -3 -2 -1 0 1 2 8 9 10 11 12 13 -6 -1 0 2 3 5 23 8 5 -1 -4 -10 -7 11 ½ 4 0 -2.1 42 114 -6.75 9 -7 -2/59 x g(x) x y x k(x) -9 -7 -5 -3 -1 1 10 6 2 2 6 10 57/16 11 102 1 2 18 1.25 3 10 undefined 0 4 -2 6 4 -1 2 10 ¼ 64 16 ½ 4 1024 2.2 Linear Equations 9. Graph y = -4x +3 10. Graph y = 3x – 5 11. Graph y = 2/3x +2 12. Graph y = -1/4x -7 13. What is the purpose of sliders using Desmos for m and b when you have y = mx + b ? 14. Do the tables represent linear functions? x g(x) x y x k(x) -4 -2 0 2 4 6 8 10 12 14 18 20 15 9 -6 6 0 12 2 -2 -12 -4 -8 0 -12 0 4 8 -12 -4 2 5 6 7 2 3 15. What is the formula for slope? 16. What is the point-slope formula? What information do you need to use this formula? What does the formula give you? 17. Parallel lines have slopes that are _________________. 18. Perpendicular lines have slopes that are ________________________. 19. Find the equation of the line that has a m = ¾ and passes through the point (-4,5). 20. Find the equation of the line that has a m = -5 and passes through the point (8,0). 21. Find the equation of the line that has passes through the points (0,4) and (-2,0). 22. Find the equation of the line that has passes through the points (-4,-4) and (0,3). 23. Find the equation of the line that passes through (3,-5) and is parallel to y = ½ x + 9. 24. Find the equation of the line that passes through (-6,8) and is perpendicular to y = ½ x+9. 25. Draw two lines that are parallel. Draw two lines that are perpendicular. 2.3 Direct Variation 26. What is the formula that models all direct variations? What is the y-intercept for all direct variations? 27. Determine if the relations below are direct variations. If they are direct, then find k. x g(x) x y x k(x) 11 3 -5 ½ 0.46 298 66 18 -3 3 2.76 1788 45 18 5/3 2.99 -7 0 33.75 13.5 1.25 2.2 -5 0 1000 100 10 1 1/10 1/100 27300 2730 273 27.3 2.73 0.273 2.4 Linear Modeling 28. There is a pizza place in Chicago called Debonairs, they are famous for huge, Chicagostyle pieces of pizza. Your first piece costs $8.00. The second piece costs $7.50. The third, $7.00, and so on. Create a linear equation that models the price for any piece of pizza. Define the variables. 29. Find the cost of pizza for you and five friends at Debonairs. 30. Franklin sells magazines to raise money for his hockey club team. For a one-time price of only $28.75, customers can subscribe to magazines for $5 each. Create a linear equation that models the total cost for any number of magazine subscriptions. Define the variables. 31. Find the cost for ordering Time, Sports Illustrated and GQ. 32. It is 603 miles from Pittsburgh to St. Louis. The Cardinals leave Pittsburgh for St. Louis at 1:30 AM on Tuesday. Their plane travels at average speed of 230 mph. Create a linear equation that models the distance the Cardinals are from St. Louis. Define the variables. 33. How are Cardinals from St. Louis at 2:45 AM on Tuesday? What is a reasonable domain and range for the equation your created? 34. Below is a table showing data collected in various countries that represent a countries entrepreneurship capabilities and student’s math scores. Use Desmos to create a scatter plot of the data and find the line of best fit. Write the equation for the line of best fit. Greece United States Germany United Kingdom France Korea Singapore Switzerland Entrepreneurship Capabilities 49.7 55.7 37.1 42.5 38.4 26.7 24.1 42.4 Math Scores 466 487 513 492 497 546 562 543 http://zhaolearning.com/2012/06/06/test-scores-vs-entrepreneurship-pisa-timss-and-confidence/ 2.5 Absolute Value Functions and Graphs *problems from this section are mixed into the other sections 2.6 Parent Functions (Families of Functions) and Transformations 35. Determine the parent function from the rule. y mx b y ( x 84) 4 4 5 2 h( x ) 1 x9 g ( x) 6 x 3 9 y 74 x 3 k ( x ) 5 x 2 f ( x) x 2 8 y 5x 8 a ( x) 1593 1 x y y1 m( x x1 ) w( x) x 3 x 2 x 1 .4 j ( x) 13.52 x 903 45 99.34 x y 12 x 1 y 8x 1 h( r ) r 3 y x 8 9 $(t ) 10,000 (1.05) t h(t ) h0 vo t 12 at 2 1 y 2 x 5 C 9 ( F 32) v(t ) v0 at F 95 C 32 p(d ) r 3 d 2 2 3 p(r ) r 3 d 2 36. Determine the parent function from the graph. 37. Determine the parent function from the table. x h(x) x y x y -1 3 -5 2 0 6 -1 27 -125 8 0 216 8 -9 45 -92 0 -15/6 8 9 45 92 0 15/6 1 6 1.2 -2 0 -9 1 36 1.44 4 0 81 x y t d(t) x m(x) 81 1 0 256 25 100 9 1 0 16 5 10 -11 4 73 2/4 -5.2 0 -11 4 73 2/3 -5.2 0 -2 -1 0 1 2 3 1/9 1/3 1 3 9 27 x p(x) x y x y) 10 6 -8 0 1 2 0.1 1/6 -1/8 ERR 1 1/2 6 9 -1 1 2 7 27 66 6 2 3 38 -1 0 1 -2 2 1 1 1 ? ? 38. Describe the transformations. Write the rule. 39. Describe the transformations. Create a graph. y ( x 3) 2 1 y x2 4 y x f ( x) 2 x 3 g ( x ) 3 x 6 1 x y 13 x 2 y 2.7 Two Variable Inequalities 40. How are open and closed circles related to dashed and solid lines? 41. For two-variable inequality graphs, when is the graph shaded up or down? 42. Graph y x 4 y 12 x 2 f ( x) x 2 5 y x 3 1

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