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Lesson 4-3Lesson 4-3Reflecting Graphs:Reflecting Graphs:
SymmetrySymmetry
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Use your grapher to sketch the following:
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Use your grapher to sketch the following:
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Use your grapher to sketch the following:
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Use your grapher to sketch the following:
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Use your grapher to sketch the following:
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Use your grapher to sketch the following:
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Use your grapher to sketch the following:
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Use your grapher to sketch the following:
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Use your grapher to sketch the following:
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Use your grapher to sketch the following:
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Use your grapher to sketch the following:
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Use your grapher to sketch the following:
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Use your grapher to sketch the following:
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Use your grapher to sketch the following:
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Use your grapher to sketch the following:
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Use your grapher to sketch the following:
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Use your grapher to sketch the following:
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Reflections over the x-axis:
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Reflections over the x-axis:
• A graph is a reflection over the x-axis if all (x, y) can be paired to (x, -y).
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Reflections over the y-axis:
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Reflections over the y-axis:
• A graph is a reflection over the y-axis if all (x, y) can be paired to (-x, y).
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Reflections over the line y = x:
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Reflections over the line y = x:
• A graph is a reflection over the line y = x if all (x, y) can be paired to (y, x).
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Reflections over the origin:
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Reflections over the origin:
• A graph is a reflection in the origin if all (x, y) can be paired to (-x, -y).
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Use symmetry to sketch the graph of:
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Use symmetry to sketch the graph of:
Think: Could you graph y = x4 ?
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Use symmetry to sketch the graph of:
Think: Could you graph y = x4 ?
So, first trade places with x and y then solve for y.
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Use symmetry to sketch the graph of:
x4 = y + 1, solve for y
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Use symmetry to sketch the graph of:
x4 = y + 1, solve for y
x4 – 1 = y
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Use symmetry to sketch the graph of:
Graph and then let every (x, y) become (y, x).
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Use symmetry to sketch the graph of:
Graph and then let every (x, y) become (y, x).
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Line of symmetry:
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Line of symmetry:
• A line that is the perpendicular bisector of any segment joining any pair of corresponding points.
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Point of symmetry:
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Point of symmetry:
• A point 0 such that it is possible to pair the points of the graph in such a way that 0 is the midpoint of the segment joining each pair.
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For quadratics:
• Axis of symmetry -
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For cubics:
• Point of symmetry -
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Assignment:
Pgs. 135-137C.E. 1-8 all,
W.E. 1-19 odd