## 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 ofandare the graphcompressed in the– direction. For example we can writeThe graph is compressed in the- direction by the factor

The above graphs are the reflections of the graphs graphsandin the- axis. The same transformation is achieved by making the swap

The transformation above are translations of the exponential curveby 2 to the left to giveand a translation of 1 to the right to giveNotice that a negative- transformation by two becomes ain the equation of the graph, and a positive translation of bybecomes ain the equation of the graph. This is because these particular transformations are– transformations, and– transformations are always counter intuitive.

The graph ofabove is the reflection of the graphin the– axis. This simple introduces a factor ofin the equation ofto give

The graphis transformed above by moving up by 3 and down by 1 (– transformations) respectively. The equation becomesandrespectively.