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**3.5 Graphs in Three Dimensions**

Graphing Points in Three Dimensions Graphing Equations in Three Dimensions

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**1) Graphing Points in Three Dimensions**

Today…we enter…the third dimension… Street artist Julian Beever Photos from:

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**1) Graphing Points in Three Dimensions**

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**1) Graphing Points in Three Dimensions**

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**1) Graphing Points in Three Dimensions**

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**1) Graphing Points in Three Dimensions**

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**1) Graphing Points in Three Dimensions**

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**1) Graphing Points in Three Dimensions**

We live in a 3D world and need a “third dimension” to describe location Example: Name the three dimensions of the figure below.

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**1) Graphing Points in Three Dimensions**

We live in a 3D world and need a “third dimension” to describe location Example: Name the three dimensions of the figure below. Answer: The figure has length, width and height.

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**1) Graphing Points in Three Dimensions**

The x-axis describes horizontal movement The y-axis describes vertical movement The z-axis describes movement somewhere in between…

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**1) Graphing Points in Three Dimensions**

How to graph in 3-dimensions… x – shift forward and backward y – shift left and right z – shift up and down

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**1) Graphing Points in Three Dimensions**

How to graph in 3-dimensions… x – shift forward and backward y – shift left and right z – shift up and down Points are communicated as (x, y, z)

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**1) Graphing Points in Three Dimensions**

Example 1: Graph (0, 3, -2).

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**1) Graphing Points in Three Dimensions**

Example 1: Graph (0, 3, -2). Answer: x = 0; no movement x -x y -y z -z

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**1) Graphing Points in Three Dimensions**

Example 1: Graph (0, 3, -2). Answer: x = 0; no movement y = 3; move right 3 units x -x y -y z -z

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**1) Graphing Points in Three Dimensions**

Example 1: Graph (0, 3, -2). Answer: x = 0; no movement y = 3; move right 3 units z = -2; move down 2 units x -x y -y z -z

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**1) Graphing Points in Three Dimensions**

Example 1: Graph (0, 3, -2). Answer: x = 0; no movement y = 3; move right 3 units z = -2; move down 2 units x -x y -y z -z (0, 3, -2)

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**1) Graphing Points in Three Dimensions**

Example 2: Graph (-3, 3, -4).

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**1) Graphing Points in Three Dimensions**

Example 2: Graph (-3, 3, -4). Answer: x = -3; move backward 3 units x -x y -y z -z

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**1) Graphing Points in Three Dimensions**

Example 2: Graph (-3, 3, -4). Answer: x = -3; move backward 3 units y = 3; move right 3 units x -x y -y z -z

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**1) Graphing Points in Three Dimensions**

Example 2: Graph (-3, 3, -4). Answer: x = -3; move backward 3 units y = 3; move right 3 units z = -4; move down 4 units x -x y -y z -z

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**1) Graphing Points in Three Dimensions**

Example 2: Graph (-3, 3, -4). Answer: x = -3; move backward 3 units y = 3; move right 3 units z = -4; move down 4 units x -x y -y z -z (-3, 3, -4)

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**1) Graphing Points in Three Dimensions**

Example 3: Find the coordinate of the point below. x -x y -y z -z

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**1) Graphing Points in Three Dimensions**

Example 3: Find the coordinate of the point below. Therefore, the solution is (2, -3, 3) x -x y -y z -z (2, -3, 3)

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Homework p.149 #1-12, 25 QUIZ: 3.1, 3.2 on WEDNESDAY

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Copyright © 2011 Pearson Education, Inc. Slide 2.2-1 2.2 Vertical Translations of Graphs Vertical Shifting of the Graph of a Function If the graph of is.

Copyright © 2011 Pearson Education, Inc. Slide 2.2-1 2.2 Vertical Translations of Graphs Vertical Shifting of the Graph of a Function If the graph of is.

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