Section 1'7 Shifting and Reflecting Graphs

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Section 1.7 Shifting and Reflecting Graphs
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What you should learn

• How to use vertical shifts to sketch graphs of
  functions
• How to use reflections to sketch graphs of
  functions

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What is the most important point?

• y x2
• (0, 0)
• y (x 0)2 0
• Suppose (3, 2)
• y (x 3)2 2

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Vertical Shifts

• Vertical shift Up c
• h(x) f(x) c
• Vertical shift Down c
• h(x) f(x) c
• In each case how much is c?

c - 4
c 3
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Horizontal Shifts

• Horizontal shift right c
• h(x) f(x c)
• Horizontal shift left c
• h(x) f(x c)
• In each case how much is c?

c 2
c - 3
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What is the equation based on y x2?
y (x 3)2 1
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What is the equation based on y x3?
y (x 2)2 3
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Reflections in the Coordinate Axis

• Reflection in the x-axis
• h(x) -f(x)

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Reflections in the Coordinate Axis

• Reflection in the y-axis
• h(x) f(-x)

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Describe the transformation of the common
function that occurs in the function. Then
sketch the graph.

• f(x) (x 2)2 3
• Horizontal Shift
• 2 to the Left
• Vertical Shift
• 3 up
• Where is the vertex
• (-2, 3)