Transformations of Linear and Absolute Value Functions Absolute Value Function Parent Function Consider the general equation If k is positive it shifts up k units If k is negative it shifts down k units ID: 503599
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Slide1
Chapter 1.2
Transformations of Linear and Absolute Value FunctionsSlide2
Absolute Value Function
Parent Function
Consider the general equation:
If k is positive, it shifts up k unitsIf k is negative, it shifts down k units
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Slide4
Absolute Value Function
Parent Function
Consider the general equation:
If h is positive, it shifts left h units
If h is negative, it shifts right h units
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Slide6
More Examples of Other Functions
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More Examples of Other Functions
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Horizontal Translations
If h > 0 then it shifts to the right
If h < 0 then it shifts to the left
Let
Rewrite the equation to the following:
Shift 3 units right
Shift 5 units left
Slide9
Horizontal Translations
If h > 0 then it shifts to the right
If h < 0 then it shifts to the left
Let
Rewrite the equation to the following:
Shift 5 units right
Shift 2 units left
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Vertical Translations
If k > 0 then it shifts up
If k < 0 then it shifts down
Let
Rewrite the equation to the following:
Shift 5 units down
Shift 7 units up
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Writing Reflections of Functions
Reflections in the x-axis:
The graph of
is a reflection in the x-axis of the graph of Reflections in the y-axis:The graph of
is a reflection in the y-axis of the graph of
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Writing Reflections of Functions
Let
Write a function whose graph is a reflection in the x-axis
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Writing Reflections of Functions
Let
Write a function whose graph is a reflection in the y-axis
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More Examples
Reflection on x-axis
Reflection on y-axis
Reflection on x-axis
Reflection on y-axis
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Stretches and Shrinks
Horizontal Stretches and Shrinks
The graph of
is a horizontal stretch or shrink by a factor of of
When 0 < a < 1 it is a shrink
When a > 1 it is a stretch
Vertical Stretches and Shrinks
The graph of
is a vertical stretch or shrink by a factor of
of
When a > 1 it is a stretchWhen 0 < a < 1 it is a shrink Slide16
Horizontal Shrink
Let
Write a function whose graph is a horizontal shrink by a factor of
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Horizontal Stretches and Shrinks
Horizontal Stretches
0 < a < 1
Horizontal Shrinksa > 1By 2:
By 3:
By 4:
By 1/2:
By 1/3:
By 1/4:
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Vertical Stretch
Let
Write a function whose graph is a vertical stretch by a factor of 3
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Vertical Stretches and Shrinks
Vertical Stretches
a
> 1Vertical Shrinks0 < a < 1By 2:
By 1/2:
By 3:
By 4:
By 1/3:
By 1/4:
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Combinations of All that Crap
Let
Write a function that represents a horizontal stretch by 4 then a shift down by 3 units
First a stretch by 4:
Then a shift down 3 units:
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Another Example
Let
Write a function that represents: Vertical stretch by 2 Then Shift down 5 units
First a stretch by 2:
Then a shift down 5 units:
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Another Example
Let
Write a function that represents:
Horizontal shrink by 6
Then Shift up 12 units
First a shrink by 6:
Then a shift up 12 units:
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Reflect over the x-axis
Multiply the whole function by -1
Reflect over the y-axis
Put a negative in front of the XHorizontal ShiftAdd or Subtract only to the XVertical ShiftAdd or Subtract from the whole functionHorizontal StretchMultiply the factor only to the X Stretch by 2 then multiply by ½ Horizontal ShrinkMultiply the factor only to the X Shrink by ½ then multiply by 2Vertical Stretch & ShrinkMultiply the whole function by the factorSlide24
Assignment
Pages 16-17
3-21 odd 23-26 all 27-31 odd