Parent Function Transformations

• Left 2; Down 1
• Reflection over x-axis; Left 2; Up 1
• Reflection over x-axis; Left 2; Down 1
• Reflection over y-axis; Right 2; Down 1

• Absolute Value
• Quadratic
• Cubic
• Linear

• Square Root
• Quadratic
• Cube Root
• Cubic

• f(x) = −(x−2)³−1
• f(x) = −(x+2)³−1
• f(x) = −(x−2)³ + 1
• f(x) = −(x+2)³ + 1

• Shift Left 4

  and

  Shift Down 6

• Shift Left 4

  and

  Shift Up 6

• Shift Right 4

  and

  Shift Down 6

• Shift Up 4

  and

  Shift Left 6

• Shift Left 2

  and

  Shift Down 3

• Shift Right 2

  and

  Shift Up 3

• Shift Right 2

  and

  Shift Down 3

• Shift Left 2

  and

  Shift Up 3

• Reflection over

  x-axis

  and

  Shift Left 5

• Reflection over

  y-axis

  and

  Shift Right 5

• Reflection over

  y-axis

  and

  Shift Up 5

• Reflection over

  x-axis

  and

  Shift Up 5

• Vertical Stretch by 2, Shift Right 3 and Shift Down 7

• Vertical Stretch by 2, Shift Right 7 and Shift Down 3

• Vertical Stretch by 2, Shift Left 7 and Shift Down 3

• Horizontal Stretch by 2, Shift Right 7 and Shift Down 3

• y = Ix + 2I - 1
• y = -Ix + 2I - 1
• y = -Ix - 2I - 1
• y = -Ix + 1I - 2

• f(x)=x² + 2
• f(x) = (x-2)² + 1
• f(x)= (x+2)² - 1
• f(x)= (x+2)² + 1