Algebra 2B NAME: _______________________________ WYNTK CH 2 (2.5 – 2.9) Test DATE: ________________ HOUR: _________

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What You Need to Know for the Chapter 2 (2.5 – 2.9) Test

A2.2.5.1 Graph linear inequalities on the coordinate plane using slope & y-intercept. Graph each inequality.

A2.2.5.2 Graph linear inequalities on the coordinate plane using intercepts. Graph each inequality using intercepts. 3. 3x + 4y ≥ 12 4. -15x + 20y < 60

A2.2.5.3 Solve problems using linear inequalities. 5. Marcus volunteers to work at a carnival booth selling raffle tickets. The tickets cost $2 each or 3 for $5. His goal is to have at least $250 in sales during his shift.

a. Let x be the number of tickets sold for $2. Let y be the number of tickets sold in sets of 3 for $5. Write and graph an inequality for the total number of tickets Marcus must sell to meet this goal.

b. If Marcus sells 75 tickets for $2 what is the least number of tickets he must sell in sets of 3 to meet his goal?

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6. Mr. and Mrs. Zaragosa are planning a landscape garden for their new house. They have set a budget of $200 for native grasses, at $12 each, and flowering plants, at $8.50 each.

a. Let n be the number of native grasses and p be the number of flowering plants. Write an inequality for the number of each they can buy.

b. Graph the inequality.

c. Describe the appropriate domain (n) and range (p). Explain how the domain and range are limited.

A2.2.5.4 Solve and graph linear inequalities Solve each inequality for y. Graph each inequality. 7. 8. A2.2.6.1 Recognize sketch and write transformations of linear functions including translation, reflection, stretch/compression and combination transformations. Graph f(x). Write the rule for g(x), using the transformation given, and then graph g(x). 9. f(x) = 3x 10. f(x) = x – 5 11. f(x) = ⅓x + 2 horizontal translation left 3 vertical compression by ⅕ reflection across the x-axis ______________________ _________________________ _____________________

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Let g(x) be the indicated combined transformation of f(x) = x. Write the rule for g(x). 12. vertical translation down 2 units followed by a horizontal compression by a factor of ⅖.

________________________ 13. horizontal stretch by a factor of 3.2 followed by a horizontal translation right 3 units.

_________________________ A.2.7.1 Fit scatter plot data using linear models with technology. 14. Vern created a website about his school’s sports teams. He has a hit counter on his site that lets him know how many people have visited the site. The table shows the number of hits the site received each day for the first two weeks. Use your graphing calculator to graph a scatter plot for the data using the day as the independent variable. Sketch the scatter plot on the graph. Use the graphing calculator to find the equation of the line of best fit.

A.2.7.2 Use linear models to make predictions. 15. A photographer hiked through the Grand Canyon. Each day she filled a photo memory card with images. When she returned from the trip, she deleted some photos, saving only the best. The table shows the number of photos she kept from all those taken for each memory card.

a. Use a graphing calculator to make a scatter plot of the data.

The independent variables is the # of photos taken.

b. Write the equation of the line of best fit.

c. Find the correlation coefficient. What does it tell you about how the line of best fit?

d. Predict the number of photos this photographer will keep if she takes 200 photos.

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A.2.8.1 Solve compound inequalities. Solve each inequality or compound inequality. Then graph the solution. 16. 17.

A.2.8.2 Write and solve absolute-value equations and inequalities. Solve each EQUATION.

18. 19.

20. 21. Solve each INEQUALITY. Then graph the solution. 22. 23.

24. 25.

26.

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A.2.9.1 Write, graph and transform absolute-value functions including translations, reflections, and stretches/compressions. Perform each transformation on f (x) = |2x| + 3. Write the transformed function g (x). 27. down 7 units. 28. reflect across the y-axis 29. left 5 units __________________ _____________________ ____________________ Translate f(x) = |x| so that the vertex is at the given point. 30. (6, -3) 31. (-2, -5) 32. (5, 8) __________________ _______________________ _____________________ Graph the original function. Then perform the transformation, write the rule for the transformed function and graph the transformed function. 33. Stretch f (x) = |3x – 6| horizontally by a factor of 3. 34. Shift f (x) = |x – 5| up 2.

35. Reflect f (x) = |x – 3|+ 2 over the x-axis.

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ANSWERS 1. dashed 2. solid

3. x = 4 and y = 3 4. x = -4 and y = 3

5. a.) 2x + 5y ≥ 250 b.) y ≥ 20 6. a.) 200 ≥ 12x + 8.5y b.) D: {x ≥ 0} & R: {y ≥ 0}

7.

€

y ≤ −32

x − 32 8.

€

y >3

10x

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9. g(x) = 3x + 9 10. g(x) = ⅕ x-1

11. g(x) = -⅓ x – 2 12.

€

g(x) =52

x −2

13.

€

g(x) =5

16x −15

16 14. y = 2.409x + 11.220

15. a.) y = 0.331x – 11.326 b.) r = 0.848 c.) about 55 16. x < 3 ; (-∞, 3)

17. x < -4 or x ≥ 4; (-∞,-4) U [4, ∞) 18. x = 3 or x = -4

19. x = ±1 20. x = 6 or x = -8 21. x = -3 or x = 11 22. X > 5 or x < -⅓; (-∞,-⅓) U (5,∞)

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23. -3 ≤ x ≤ 3; [-3,3] 24. NO SOLUTION;

25. ALL REAL NUMBERS; R 26.

€

−1< x <79

; −1 , 79

#

$ %

&

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27. g(x) = | 2x | - 4 28. g(x) = | -2x | + 3 29. g(x) = | 2x + 10 | + 3 30. g(x) = | x – 6 | - 3 31. g(x) = |x + 2| - 5 32. g(x) = | x – 5 | + 8 33. g(x) = | x – 6| 34. g(x) = |x – 5 | + 2

35. g(x) = - |x – 3| - 2