Transformations to Parent Functions

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Transformations to Parent Functions
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Translation (Shift)

• A vertical translation is made on a function by
  adding or subtracting a number to the function.
• Example y x 3 (translation up)
• Example y x² - 5 (translation down)
• A translation up is also called a vertical shift
  up.
• A translation down is also called a vertical
  shift down.

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Example y x 2

• Parent function (y x) shown on graph in red.

The transformation of the parent function is
shown in blue. It is a shift up (or vertical
translation up) of 2 units.)
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Example y x - 1

• Parent function (y x) shown on graph in red.

The transformation of the parent function is
shown in blue. It is a shift down (or vertical
translation down) of 1 unit.
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Reflection

• A reflection on the x-axis is made on a function
  by multiplying the parent function by a negative.
  
• Multiplying by a negative flips the graph of
  the function over the x-axis.
• Example y -x² is a reflection of the parent
  function y x².

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Example y - x²
The reflection of the parent function is shown in
blue. It is a reflection over the x-axis of the
function y x²
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Stretch

• A stretch is made on a parent function by
  multiplying the parent function by a number x
  such that
• x gt 1.
• Example y 3x²
• A stretch is also referred to as a narrowing of
  the graph of the function closer to the y-axis.

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Example y 2x
The blue line shows the graph of the stretch of
the parent function, y 2x, by a scale factor
of 2.
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Shrink

• A shrink is made on a function by multiplying the
  parent function by a number x such that 0 lt x
  lt 1.
• Example y (½) x.
• A shrink is also referred to as a widening of the
  graph of the function closer to the x-axis.

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Example y (¼) x
The blue line shows the graph of the shrink of
the parent function, y (¼)x, by a scale factor
of ¼.
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What happens when we combine the two (blue is
parent function)?