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**Lesson 8.3 Reflecting Points and Graphs**

To explore reflections and combinations of reflections and translations To write equations for these transformations and list definitions that describe them.

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Flipping Graphs In this investigation you will explore the relationship between the graph of an equation and its image when you flip it two different ways. Name the coordinates of the vertices of this triangle. Graph the triangle on your calculator. Use L1 for the x- coordinate of the vertices and L2 for the y-coordinates of the vertices.

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**Graph the second triangle whose vertices are listed in L3 and L4. **

Define L3 and L4 L3 = -L1 L4 = L2 Graph the second triangle whose vertices are listed in L3 and L4. Name the coordinates of the second triangle. Describe the transformation. How did the coordinates of the vertices change?

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**Graph the second triangle whose vertices are listed in L3 and L4. **

Define L3 and L4 L3 = L1 L4 = -L2 Graph the second triangle whose vertices are listed in L3 and L4. Name the coordinates of the second triangle. Describe the transformation. How did the coordinates of the vertices change?

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**Graph the second triangle whose vertices are listed in L3 and L4. **

Define L3 and L4 L3 = -L1 L4 = -L2 Graph the second triangle whose vertices are listed in L3 and L4. Name the coordinates of the second triangle. Describe the transformation. How did the coordinates of the vertices change?

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**Next you’ll see if what you have learned about flipping points is true for graphs of functions.**

Graph y = 2x on your calculator. Replace x with –x in the function. Graph this second function. Describe how the second graph is related to the graph of y = 2x .

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**Describe how the third graph is related to the graph of y = 2x. **

Replace y with –y in the function y = 2x and solve for y. Graph this third function. Describe how the third graph is related to the graph of y = 2x. Let the parent functions be Y=(x-2)2 Y=|x| Y=x Make a note of each graph and any change in the graph. Summarize what you have learned about flipping graphs.

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Examples The bold graph is the parent function y = -5+x. Describe the transformation and then write the function for the thin graph.

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**The bold graph is the parent function y =|x|**

The bold graph is the parent function y =|x|. Describe the transformation and then write the function for the thin graph.

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Find the slope of the tangent line to the graph of f at the point ( - 1, 10 ). f ( x ) = 6 - 4x 1234567891011121314151617181920 2122232425262728293031323334353637383940.

Find the slope of the tangent line to the graph of f at the point ( - 1, 10 ). f ( x ) = 6 - 4x 1234567891011121314151617181920 2122232425262728293031323334353637383940.

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