Graph the exponential function y = 2^x and its inverse y = log base 2 of x.

The given $y$ values are $-3, -2, -1, 0, 1, 2, 3$. We calculate $x$ for each $y$:

• If $y = -3$, $x = 2^{-3} = \frac{1}{8}$
• If $y = -2$, $x = 2^{-2} = \frac{1}{4}$
• If $y = -1$, $x = 2^{-1} = \frac{1}{2}$
• If $y = 0$, $x = 2^0 = 1$
• If $y = 1$, $x = 2^1 = 2$
• If $y = 2$, $x = 2^2 = 4$
• If $y = 3$, $x = 2^3 = 8$

The completed table of values is:

Plot the points from the table: $(\frac{1}{8}, -3)$, $(\frac{1}{4}, -2)$, $(\frac{1}{2}, -1)$, $(1, 0)$, $(2, 1)$, $(4, 2)$, $(8, 3)$. Draw a smooth dashed curve through these points. This curve represents $y = \log_2 x$.

Since $y = 2^x$ is the inverse of $y = \log_2 x$, its points are obtained by swapping the $x$ and $y$ coordinates from the table in Step 1. The points for $y = 2^x$ are: $(-3, \frac{1}{8})$, $(-2, \frac{1}{4})$, $(-1, \frac{1}{2})$, $(0, 1)$, $(1, 2)$, $(2, 4)$, $(3, 8)$. Draw a smooth solid curve through these points. This curve represents $y = 2^x$.

Draw a straight line passing through the origin $(0,0)$ with a slope of 1. This line acts as the axis of symmetry between the graph of a function and its inverse.

The final graph will show the exponential function $y=2^x$ (solid curve), the logarithmic function $y=\log_2 x$ (dashed curve), and the line $y=x$ (typically a dashed or dotted line for reference), demonstrating their inverse relationship as mirror images across $y=x$.