Return to Assignments Exponential functions and graphs

### Assignment 4

Draw the graph of the function:

What is the formula of the asymptote?

### Solution

Here the base is less than and therefore the graph is the mirror of the graph of the function:

We can show this quite easily. We write:

This means that the graph is the mirror in the -axis of the graph of:

The asymptote is the -axis, i.e. , because the larger the value of the more the graph approaches the -axis. We can verify this in the figure.