Exponential Functions and Graphs

Exponential graphs

$y = a^x$ and its graph, for simple positive values of $a$.

Make sure you know what the graph of $y = a^x$ looks like for different values of $a$. Look carefully at $0 < a < 1$ and $a = 1$ and $1 < a$ and make sure you can explain their features. What happens to the graphs as $a$ gets bigger and bigger? Use a graph drawing package [e.g., DESMOS GRAPHING] to help you if necessary but make sure you think through the results in each and every case.

Notice that we do not look at cases when $a < 0$. We discussed why we do not look at this case in the discussions earlier when we looked at indices so it might be useful to revisit that discussion.