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

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Presentation on theme: "2.6 Families of Functions 1.Translations 2.Stretches, Shrinks and Reflections."— Presentation transcript:

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

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?

3 2) Stretches and Shrinks Shrink Graph is SHORTER, WIDER Stretch Graph is TALLER, NARROWER

4 2) Stretches For stretches, y = a|x| a > 1

5 2) Stretches For stretches, y = a|x| a > 1 a is SLOPE

6 2) Stretches Example 1: Graph y = 2|x|.

7 2) Stretches Example 1: Graph y = 2|x|. y = 2|x| Slope = Vertex =

8 2) Stretches Example 1: Graph y = 2|x|. y = 2|x| Slope = 2 Vertex = (0, 0)

9 2) Stretches Example 1: Graph y = 2|x|. Step 1: Plot the vertex

10 2) Stretches Example 1: Graph y = 2|x|. Step 1: Plot the vertex Step 2: Use slope to plot points

11 2) Stretches Example 1: Graph y = 2|x|. Step 1: Plot the vertex Step 2: Use slope to plot points

12 2) Stretches Example 1: Graph y = 2|x|. Step 1: Plot the vertex Step 2: Use slope to plot points

13 2) Stretches Example 1: Graph y = 2|x|. Step 1: Plot the vertex Step 2: Use slope to plot points

14 2) Stretches Example 2: Write an equation for the graph below.

15 2) Stretches Example 2: Write an equation for the graph below. Vertex = Slope =

16 2) Stretches Example 2: Write an equation for the graph below. Vertex = (0, 0) Slope = 4, -4

17 2) Stretches Example 2: Write an equation for the graph below. Vertex = (0, 0) Slope = 4 y = -4|x|

18 2) Shrinks …kind of like you stepped on the graph…

19 2) Shrinks For shrinks, y = a|x| 0 < a < 1

20 2) Shrinks Example 1: Draw the graph of y = -0.5|x|.

21 2) Shrinks Example 1: Draw the graph of y = -0.5|x|. slope = 0.5 = 1 2 vertex = (0, 0) opens DOWN

22 2) Shrinks Example 1: Draw the graph of y = -0.5|x|.

23 2) Shrinks Example 1: Draw the graph of y = -0.5|x|. Slope = 1 2

24 2) Shrinks Example 1: Draw the graph of y = -0.5|x|. Slope = 1 2

25 2) Shrinks Example 1: Draw the graph of y = -0.5|x|. Slope = 1 2

26 2) Shrinks Example 2: Graph y = -0.75|x – 2| + 2

27 Example 2: Graph y = |x – 2| + 2 slope = 0.75 shift RIGHT 2 shift UP 2 = 3 4 2) Shrinks Opens DOWN

28 2) Shrinks Example 2: Graph y = -0.75|x – 2| + 2 Vertex = (2, 2) Slope = 3 4

29 2) Shrinks Example 2: Graph y = -0.75|x – 2| + 2 Vertex = (2, 2) Slope = 3 4

30 2) Shrinks Example 2: Graph y = -0.75|x – 2| + 2 Vertex = (2, 2) Slope = 3 4

31 2) Shrinks Example 2: Graph y = -0.75|x – 2| + 2 Vertex = (2, 2) Slope = 3 4

32 Homework p.98 #17, 19, 22, 25, 34, 36, 43-45, 49 QUIZ: Tuesday Sept 29 TEST: Chapter 2 Friday Oct 2 (I know you have a Literature test… but trust me, its better this way).


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