Graph the exponential function y=2x and its inverse y=log2x?

To graph the exponential function y=2^x, we can plot a few points and then connect them with a smooth curve.

When x=0, y=2^0=1
When x=1, y=2^1=2
When x=2, y=2^2=4
When x=-1, y=2^-1=1/2
When x=-2, y=2^-2=1/4

Plotting these points and connecting them with a smooth curve, we get the graph of y=2^x.

Now, to graph the inverse function y=log2(x), we can switch the x and y values of the exponential function and solve for y.

So, the inverse function is x=2^y, which can be rewritten as y=log2(x).

Plotting the inverse function on the same graph as the exponential function, we get the following graph:

The exponential function y=2^x is the curve that increases rapidly as x increases, while the inverse function y=log2(x) is the curve that increases slowly as x increases. The two functions are reflections of each other across the line y=x.

Graph of y=2^x and y=log2x

[Image of the graphs of y=2^x and y=log2x]

Steps to Graph:

1. Graph y=2^x:

- Make a table of values: (x, y) = {(0, 1), (1, 2), (2, 4), (3, 8)}
- Plot the points and connect them with a smooth curve.

2. Graph y=log2x:

- Reflect the graph of y=2^x across the line y=x.
- This is because the inverse of y=2^x is given by y=log2x.

Properties:

- Asymptote:
- y=2^x: x-axis
- y=log2x: y=0
- Range:
- y=2^x: (0, ∞)
- y=log2x: (-∞, ∞)
- Domain:
- y=2^x: (-∞, ∞)
- y=log2x: (0, ∞)