1.3- Transformations

Section 1.3 explains the different types of transformations in graphs.

The first type is a translation- a shift in the graph (left/right or up/down)
          When adding or subtracting from y, the graph moves up or down, for example,

This is the graph of  shifted up ten units 

This is the graph of  shifted down ten units

      

         When adding or subtracting from x, the graph moves left or right, for example,

                    The graph moves to the right when c is negative.

This is the graph of  shifted to the right ten units

                   

                     The graph would move to the left if c were positive.

This is the graph of  shifted to the left ten units

The second type is a dilation- a change in the shape of the graph 

          To vertically shrink the graph, multiply y by a number less than one but greater than zero.

Where,

          To vertically stretch the graph, multiply y by a number greater than one. 

Where, 

        To horizontally shrink the graph, multiply x by a number greater than one. The opposite is true to stretch the graph, multiply x by a number less than one but greater than zero. For example,

The third type is a reflection- a change about the x or y axis

          To reflect upon the x-axis, multiply the y values by -1

          To reflect upon the y-axis, multiply the x value by -1