## Finding Asymptotes For Exponential Graphs

We can usually sketch exponential graphs by finding the asymptotes and the intersections of the graph with the axes. This is because all exponential graphs have the same basic shape. Any exponential curve can be obtained by reflecting, rotating and stretching.

To find the intersections with the axis, put each coordinate equal to 0.

If we find the intersection with the – axis by putting We find the – intersection by putting This has no real solution but since tends to 0 for tending to we can take the – intercept to be at To find the equation of the asymptote(s) put and successively equal to Putting implies and vice versa, so this gives us no asymptote. Put to get Putting returns nothing for since has no solution for  If we find the intersection with the – axis by putting We find the – intersection by putting To find the equation of the asymptote(s) put and successively equal to Putting implies and vice versa, so this gives us no asymptote. Put to get Putting returns nothing for since has no solution for   