Algebra 2 1 st Nine Weeks Review Inequalities

Algebra 2 1 st Nine Weeks Review

Inequalities and Absolute Value Things to Remember Inequalities ØSolves like an equation ØSpecial Rule: reverse the inequality when you x or by a negative ØGraph by reading the inequality symbols Absolute Value Equations Absolute Value Inequalities ØSet up 2 equations to represent the + and – cases. ØCombines the rules for Absolute Value and Inequalities. ØSolve each eqution ØSet up 2 inequalities and solve. ØGraph answers as points on the number line ØSpecial Rule: reverse the inequality when set up the ØSpecial Rule: Check for negative case. extraneous solutions.

Practice!!!! (Copy and work on your paper while volunteers work on board. ) 6 x – 10 ≤ 14 |5 x – 10 | = 45 – 1 < 2 x + 7 < 19 |2 x + 12 | = 4 x x + 4 ≤ 9 or or x – 3 ≥ 7 |3 x – 2| 13

Practice!!!! (Copy and work on your paper while volunteers work on board. ) 6 x – 10 ≤ 14 |5 x – 10 | = 45 – 1 < 2 x + 7 < 19 |2 x + 12 | = 4 x x + 4 ≤ 9 or x – 3 ≥ 7 |3 x – 2| 13

SCATTER PLOTS True or False a quick quiz 1. The data in scatter plots is discrete. 2. The line of best fit must go through at least 2 points. 3. When asked for domain and range, you can just list the headings in the table. (ie. Height, weight…) 4. The correlation coefficient of data describes how closely “lined up” data points are what direction they go.

SCATTER PLOTS True or False a quick quiz T 1. The data in scatter plots is discrete. F 2. The line of best fit must go through at least 2 points. F 3. When asked for domain and range, you can just list the headings in the table. (ie. Height, weight…) 4. The correlation coefficient of data T describes how closely “lined up” data points are what direction they go.

PRACTICE!!!!! For the data in the table above a. Find the line of best fit. b. Graph the data with the line of best fit. c. Name the type of data. d. Name the correlation. Estimate the correlation coefficient. e. Give the domain and range of the data.

PRACTICE!!!!! For the data in the table above a. Find the line of best fit. b. Graph the data with the line of best fit. c. Name the type of data. DISCRETE d. Name the correlation. Estimate the correlation coefficient. POSITIVE r=. 5 e. Give the domain and range of the data. D: 37. 8, 19. 2, 21. 3, 26. 2, 26. 8 R: 140, 45, 78, 121, 105

Function Operations / Compositions 3 types Evaluation g(10) = value you get when you substitute 10 into g(x). g(10) = -3(10) + 1 Operations Add or subtract by combining like terms. Multiply by distributing. f(3) + g(5) = (2 -(3) 2 ) + (-3(5) + 1) -7 -14=-21 g(2) f(-2) (-3(2) + 1) (2 – (-2) 2) (-5) (-2) 10 Compositions f(g(5)) = value you get when you substitute g(5) into f(x). g(3) = -3(3) + 1 = -8 f(-8) = 2 -(-8)2=-62

PRACTICE

Domain and Range Tell what’s different about each, name D and R, tell if it is a function, whether it is discrete or continuous.

Domain and Range Tell what’s different about each, name D and R, tell if it is a function, whether it is discrete or continuous. Domain: -6≤x ≤ 6 Range: 0 ≤ y ≤ 6 Domain: x ≥ 0 Range: all real numbers Domain: -3 x 4 Range: 0 ≤ y 5 Domain: -5, -4, -2, 0, 3, 5 Range: -1, 0, 2, 3, 4, 5

y a l p t’s Le Name the TRANSFORMATION Match the equation to the correct description. a. Stretch by factor of 2, right 3, down 7 b. Vertical Reflection, stretch by a factor of 2, left 7, up 3. c. Vertical Reflection, shrink by a factor of ½, left 3, up 7. d. Stretch by a factor of 2, right 7, down 3. e. Vertical Reflection, Stretch by a factor of 2, left 3, up 7.

Transformation Extension If this graph is … then what would the equation of this graph be?