Absolute Value Function Transformations

• It controls the vertical translation by shifting the graph up or down.

• It controls the horizontal translation by shifting the graph left or right.

• It is the x-coordinate of the vertex.

• The opposite of k is the x-coordinate of the vertex.

• It is the y-coordinate of the vertex.

• It controls the vertical translation by shifting the graph up or down.

• It controls the horizontal translation by shifting the graph left or right.

• It is the x-coordinate of the vertex.

• The opposite of h is the x-coordinate of the vertex.

• It is the y-coordinate of the vertex.

• -a will cause the graph to move down.

• -a will cause the graph to move left.

• -a will cause the graph to reflect over the x-axis.

• -a will cause the graph to reflect over the y-axis.

• If a is bigger than 1, the graph gets wider.

• If a is smaller than -1, the graph gets narrower.

• If a is bigger than 1, the graph gets narrower.

• If a falls between -1 and 1, the graph will get wider.

Match each equation to its vertex.

Group the absolute value equations by type of dilation.

Groups:

(a) No Dilation

,

(b) Dilation = Narrower

,

(c) Dilation = Wider

Sort the absolute value equations into the appropriate direction of opening categories.

Groups:

(a) YES Reflection - Opens Down

,

(b) NO Reflection - Opens Up

• Translation: left 1, down 1

  Reflection: over the x-axis

  Dilation: wider

• Translation: right 1

  Reflection: over the x-axis

  Dilation: wider

• Translation: left 1

  Reflection: over the x-axis

  Dilation: narrower

• Translation: right 1

  Reflection: none

  Dilation: narrower

• Translation: up 5

  Reflection: none

  Dilation: wider

• Translation: right 6, down 1

  Reflection: over the x-axis

  Dilation: narrower

• Translation: left 6, down 1

  Reflection: none

  Dilation: narrower

• Translation: left 6, up 1

  Reflection: over the x-axis

  Dilation: wider

• Translation: left 2, up 4

  Reflection: none

  Dilation: wider

• Translation: left 2, down 4

  Reflection: over the x-axis

  Dilation: none

• Translation: right 2, up 4

  Reflection: over the x-axis

  Dilation: none

• Translation: right 2, up 4

  Reflection: over the x-axis

  Dilation: narrower