## Transforming Graphs of Exponential Functioins

All exponential function graphs have the same shape, which may nevertheless be rotated, stretched or rotated to give some other exponential graph. The above graphs of and are the graph compressed in the – direction. For example we can write The graph is compressed in the - direction by the factor  The above graphs are the reflections of the graphs graphs and in the - axis. The same transformation is achieved by making the swap  The transformation above are translations of the exponential curve by 2 to the left to give and a translation of 1 to the right to give Notice that a negative - transformation by two becomes a in the equation of the graph, and a positive translation of by becomes a in the equation of the graph. This is because these particular transformations are – transformations, and – transformations are always counter intuitive. The graph of above is the reflection of the graph in the – axis. This simple introduces a factor of in the equation of to give  The graph is transformed above by moving up by 3 and down by 1 ( – transformations) respectively. The equation becomes and respectively. 