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Math 10 Absolute Value Worksheet - Answers 1. State the transformations, mapping rule and new table of values. State the vertex and equation of the axis of symmetry and then, draw the graph. a) y + 3 = |x – 1| Transformations: VT = -3, HT = 1 Mapping Rule: Vertex: (x, y) (x + 1, y – 3) (1, -3) Table of Values: Axis: x = 1 x -2 -1 0 1 2 3 4 y 0 -1 -2 -3 -2 -1 0 b) -(y – 1) = |x +3| Transformations: VT = 1, HT = -3, Rx Mapping Rule: Vertex: (x, y) (x - 3, -y + 1) (-3, 1) Table of Values: Axis: x = -3 x -6 -5 -4 -3 -2 -1 0 y -2 -1 0 1 0 -1 -2 c) 2(y + 1) = |x| Transformations: VT = -1, VS = ½ Mapping Rule: Vertex: (x, y) (x, ½y – 1) (0, -1) Table of Values: Axis: x = 0 x -3 -2 -1 0 1 2 3 y ½ 0 -½ -1 -½ 0 ½ 2. State the transformations applied to y = |x| based on the given mapping rule: a) (x, y) (x – 2, -3y) b) (x, y) (x, ½ y + 3) HT = -2, Rx, VS = 3 VS = ½, VT = 3 c) (x, y) (x + 5, -2y – 5) HT = 5, Rx, VS = 2, VT = -5 3. State the equation given the following transformations (applied to y = |x|): a) VT = -1, VS = 4, HT = 3 ¼ (y + 1) = |x – 3| b) Rx, VT = 3 c) Rx, HT = -4, VT = 2 -(y – 3) = |x| -(y - 2) = |x + 4| 4. State the transformations and then the equation for: A) Transformations: VT = 2, HT = 4 Equation: y – 2 = |x – 4| B) Transformations: VT = -2, HT = - 1, VS = ½ Equation: 2(y + 2) = |x + 1| C) Transformations: Rx, VT = -3, HT = 2 Equation: -(y + 3) = |x – 2|