The plot above shows the graphs of $f(x) = 2^x$ (in blue) and $f(x) = 2^{-x}$ (in red, dashed). Here's a summary of their behavior:

• For $f(x) = 2^x$: As $x$ becomes negative, the values get smaller and approach zero but never reach it. As $x$ increases positively, the function grows rapidly.
• For $f(x) = 2^{-x}$: This function is a reflection of $2^x$ over the y-axis. It decreases rapidly as $x$ increases, but approaches zero for large negative values of $x$.

Would you like more details, or have any questions about these functions?

Here are 5 related questions you might find helpful:

1. How does the behavior of $3^x$ compare to $2^x$?
2. What happens to the function $2^x$ when $x$ approaches infinity?
3. What is the derivative of $2^x$ and how does it relate to the function's growth?
4. Can you describe the behavior of $f(x) = a^x$ for values of $a$ between 0 and 1?
5. How do the graphs of logarithmic functions relate to these exponential functions?

Tip: When $x$ is negative in an exponential function $a^x$, the result is equivalent to $\frac{1}{a^{|x|}}$, which tends to 0 as $x$ becomes more negative for $a > 1$.