2.6 Families of Functions 1.Translations 2.Stretches, Shrinks and Reflections

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Transcript of 2.6 Families of Functions 1.Translations 2.Stretches, Shrinks and Reflections

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2.6 Families of Functions 1.Translations 2.Stretches, Shrinks and Reflections Slide 2 2) Stretches and Shrinks Stretching a rubber band vertically makes it longer Releasing or shrinking it makes it wider Stretching and shrinking a graph is the same idea What does it look like? Slide 3 2) Stretches and Shrinks Shrink Graph is SHORTER, WIDER Stretch Graph is TALLER, NARROWER Slide 4 2) Stretches For stretches, y = a|x| a > 1 Slide 5 2) Stretches For stretches, y = a|x| a > 1 a is SLOPE Slide 6 2) Stretches Example 1: Graph y = 2|x|. Slide 7 2) Stretches Example 1: Graph y = 2|x|. y = 2|x| Slope = Vertex = Slide 8 2) Stretches Example 1: Graph y = 2|x|. y = 2|x| Slope = 2 Vertex = (0, 0) Slide 9 2) Stretches Example 1: Graph y = 2|x|. Step 1: Plot the vertex Slide 10 2) Stretches Example 1: Graph y = 2|x|. Step 1: Plot the vertex Step 2: Use slope to plot points Slide 11 2) Stretches Example 1: Graph y = 2|x|. Step 1: Plot the vertex Step 2: Use slope to plot points Slide 12 2) Stretches Example 1: Graph y = 2|x|. Step 1: Plot the vertex Step 2: Use slope to plot points Slide 13 2) Stretches Example 1: Graph y = 2|x|. Step 1: Plot the vertex Step 2: Use slope to plot points Slide 14 2) Stretches Example 2: Write an equation for the graph below. Slide 15 2) Stretches Example 2: Write an equation for the graph below. Vertex = Slope = Slide 16 2) Stretches Example 2: Write an equation for the graph below. Vertex = (0, 0) Slope = 4, -4 Slide 17 2) Stretches Example 2: Write an equation for the graph below. Vertex = (0, 0) Slope = 4 y = -4|x| Slide 18 2) Shrinks kind of like you stepped on the graph Slide 19 2) Shrinks For shrinks, y = a|x| 0 < a < 1 Slide 20 2) Shrinks Example 1: Draw the graph of y = -0.5|x|. Slide 21 2) Shrinks Example 1: Draw the graph of y = -0.5|x|. slope = 0.5 = 1 2 vertex = (0, 0) opens DOWN Slide 22 2) Shrinks Example 1: Draw the graph of y = -0.5|x|. Slide 23 2) Shrinks Example 1: Draw the graph of y = -0.5|x|. Slope = 1 2 Slide 24 2) Shrinks Example 1: Draw the graph of y = -0.5|x|. Slope = 1 2 Slide 25 2) Shrinks Example 1: Draw the graph of y = -0.5|x|. Slope = 1 2 Slide 26 2) Shrinks Example 2: Graph y = -0.75|x 2| + 2 Slide 27 Example 2: Graph y = - 0.75|x 2| + 2 slope = 0.75 shift RIGHT 2 shift UP 2 = 3 4 2) Shrinks Opens DOWN Slide 28 2) Shrinks Example 2: Graph y = -0.75|x 2| + 2 Vertex = (2, 2) Slope = 3 4 Slide 29 2) Shrinks Example 2: Graph y = -0.75|x 2| + 2 Vertex = (2, 2) Slope = 3 4 Slide 30 2) Shrinks Example 2: Graph y = -0.75|x 2| + 2 Vertex = (2, 2) Slope = 3 4 Slide 31 2) Shrinks Example 2: Graph y = -0.75|x 2| + 2 Vertex = (2, 2) Slope = 3 4 Slide 32 Homework p.98 #17, 19, 22, 25, 34, 36, 43-45, 49 QUIZ: 2.5-2.7 Tuesday Sept 29 TEST: Chapter 2 Friday Oct 2 (I know you have a Literature test but trust me, its better this way).