Transformation

Graphs can be reflected through the x or y axis and also through the origin.
If graphs are reflected then one of the following must be true:

• Reflection through the x axis requires that if coordinates (3,4) are on the original graph
  then coordinates (3,-4) are on the reflected graph. ie if (a,b) then (a,-b)


• Reflection through the y axis requires that if coordinates (3,4) are on the original graph
  then coordinates (-3,4) are on the reflected graph. ie if (a,b) then (-a,b)


• Reflection through the origin requires that if coordinates (3,4) are on the original graph
  then coordinates (-3,-4) are on the reflected graph. ie if (a,b) then (-a,-b)

This is the function y = (x-1)² + 2







This is the function y = (x-1)² + 2 and its reflection y = (x+1)² + 2 through the y axis.
Notice that for every (x,y) coordinates there is an (-x,y).







  This is the graph of y = (x - 2)³.
  What is it reflected across the y axis? Try to draw the graph before checking the answer.  answer

  What is it reflected across the x axis? Try to draw the graph before checking the answer.   answer




  This is the graph of y = 1/x.   x ≥ 0
  What is it reflected across the origin? Try to draw the graph before checking the answer.   answer




Moving the graph to another place but not changing the graph's shape is called a rigid transformation

Next we will study nonrigid transformation which means that the graph's shape will change.  next

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