Make a list with two columns for x- and y-coordinates. In the x column, fill in values of x you want to show on your graph. In the y column, use the given function to calculate the values of y corresponding to each value of x. For example, if your function is y = 2^x, your table might be:
x, y
-10, 0.001
-5, 0.031
-3, 0.125
-2, 0.25
-1, 0.5
0, 1
1, 2
2, 4
3, 8
4, 16
Draw the x- and y-coordinate axes and label the axes with values so that most of your points will fit on the graph. In the given example, you might choose values ranging from -10 to 10 for both the x- and y-axes since the point (4, 16) is the only one that will not fit. Calculating (4, 16) is still useful because it gives you a better idea of the graph's direction after (3, 8).
Plot the x- and y-coordinates on the graph and connect them with a smooth curve. Extend the curve to the edge of the graph. If you are unsure about how the graph should look at a particular point, calculate more coordinates as needed.
Plot the inverse function by swapping every x for a y. In the given example, the inverse function includes the points (0.001, -10), (0.008, -7), (0.031, -5), etc. Algebraically, it is y = log2(x), where log2 signifies the base-2 logarithm of x. Connect the points with a smooth curve as you did with the original function. The inverse function should look like a mirror image of the original function across the line y = x.