TRANSFORMATIONS

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TRANSFORMATIONS
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The following are what we call

• The Parent Functions

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f(x) c
Constant Function
f(x) x
Linear Function
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f(x) x
Absolute Value Function
f(x)
Square Root Function
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f(x) x2
Quadratic Function
f(x) x3
Cubic Function
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What happens when we change the equations of
these parent functions?
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Parent Function
relative function
change?
y1 x
y2 x 2
Up 2
y2 x - 3
y1 x
Down 3
y1 x
y2 x 5
Up 5
y1 x
y2 x - 1
Down 1
Now, make a conclusion
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Describe the Shift
up 14
Down 3
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• What did the negative on the outside do?

Reflection in the x-axis
-(x)
Study tip If the sign is on the outside it has
x-scaped

• What do you think the negative on the inside will
  do?

Reflection in the y-axis
(-x)
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What word do we use to describe what as happened
to these functions?

• These have all been examples of rigid
  transformations, because they do not change shape.

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Nonrigid Transformations

• What is this? This is a transformation that
  causes distortion to the original graph!
• What do we do to an equation to make this happen?
  We put a number in front or on the inside of the
  parent function.

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Nonrigid Transformations
Vertical stretch
c gt1
f(x) 3x²
Closer to y-axis
0 lt c lt 1
Vertical shrink
f(x) ½ x²
Closer to x-axis
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Describe the Shift
Reflection over x-axis, down 6
Vertical shrink, Up 7
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Quadratic
Absolute Value
Square Root
Cubic
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Classwork/Homework Worksheets

• Transformations