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.

Ifwe find the intersection with the– axis by putting

We find the– intersection by puttingThis has no real solution but since tends to 0 fortending towe can take the– intercept to be at

To find the equation of the asymptote(s) putandsuccessively equal to

Puttingimpliesand vice versa, so this gives us no asymptote. Put to getPuttingreturns nothing forsincehas no solution for

Ifwe find the intersection with the– axis by putting

We find the– intersection by putting

To find the equation of the asymptote(s) putandsuccessively equal to

Puttingimpliesand vice versa, so this gives us no asymptote. Put to getPuttingreturns nothing forsincehas no solution for