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Do-Now: Please check your homework with the answer key provided on the side table Choose 2 problems from the word problems review & complete. The function f(x) is graphed below. Another function, g(x) is defined by the rule g(x)= x+2. Which of the following is true? Check all that apply f(0) = 2 g(-1) = f(2) g(0) < f(0) g(0) > f(0) g(-2) + f(1) =0 g(6) – f(2) = 4 Solve and graph the following: -2x+3 > 15 x < -6 Solve and graph the following: |2x-5| + 6 > 15 x < -2 OR x>7 Solve and graph the following: -3|4x|> 33 No solution Solve and graph the following: 15 ≤ 2𝑥 − 5 < 23 10 ≤ x<14 Solve for a: 𝑥 + 𝑏 = 2𝑎𝑐 𝒙+𝒃 𝒂= 𝟐𝒄 Solve for w: 2 1 = 𝑥−4 𝑤+𝑐 −𝟐𝒄 + 𝒙 − 𝟒 𝒘= 𝟐 Solve for x: 𝑎(𝑥 + 1) = 3𝑤𝑦𝑧 x= 𝟑𝒘𝒚𝒛 𝒂 −𝟏 What is the slope of the line 2x – 3y = 7 𝟐 𝟑 What is the slope of each of the following lines? Y = 10 b) X = -4 a) A) zero B) undefined Graphically speaking, a function must pass the _______________ ____________ Test. Vertical Line Test In relating the miles driven in a rental car to the total cost of the rental, which is the dependent variable? Which is the independent variable? Independent: x = # of miles Dependent: y = total cost of rental a) b) c) d) (-3, 5) (1, 6) (2, -6) (5, 0) x -3 2 5 y 2 6 3 If y = 2x + 1 find the corresponding range values for the domain D: {-3, 0, 1, 5) {-5, 1, 3, 11} 𝑨&𝑪 Draw the following relation as a mapping diagram: {(0,1), (2,-3), (3, 4), (2, 2)} Is this relation a function? No, each domain value is not paired with one range value. (“Domain repeats”) A) B) C) an equation with one solution an equation with no solution an equation with infinitely many solutions 𝑬𝑿: 𝑨) 𝟓𝒙 = 𝟏𝟎 𝑩) 𝒙 + 𝟏 = 𝒙 + 𝟓 𝑪) 𝒙 + 𝟏 = 𝒙 + 𝟏 What is the slope between (2,3) and (-1,4)? 1 m = −3 What is the equation of the linear function (in y=mx+b form) of the line that passes through the point (6,3) and is parallel to the line 2x – 4y=8? 1 𝑦= 𝑥 2 What is the relationship between the slopes and y-intercepts of parallel lines? 𝑆𝑎𝑚𝑒 𝑠𝑙𝑜𝑝𝑒 & 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑡 𝑦 − 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡𝑠 What is the relationship between the slopes and y-intercepts of perpendicular lines? 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑟𝑒𝑐𝑖𝑝𝑟𝑜𝑐𝑎𝑙 𝑠𝑙𝑜𝑝𝑒, 𝑛𝑜 𝑟𝑒𝑠𝑡𝑟𝑖𝑐𝑡𝑖𝑜𝑛 𝑜𝑛 𝑡ℎ𝑒 𝑦 − 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡𝑠 The slope Line A is 0, what is the slope of the line perpendicular to Line A? 𝑢𝑛𝑑𝑒𝑓𝑖𝑛𝑒𝑑 Are the following lines parallel, perpendicular, or neither? 2x – 4y = 8 3x + 8y = 16 𝑛𝑒𝑖𝑡ℎ𝑒𝑟 Are the following lines parallel, perpendicular, or neither? 3x – 6y = 10 2x – 4y = 30 𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙 𝑦>𝑥−2 3 𝑦 > 𝑥+3 2 3 𝑦 < 𝑥−2 2 1 𝑦 ≤ 𝑥−1 2 𝑦 > 2𝑥 − 4 Bob starts out in his car traveling 30 mph. Four hours later, Fenster starts out from the same point at 60 mph to overtake Bob. In how many hours will Fenster catch him? Fenster will catch him in 8 hours.