The image shows two functions:

1. $f(x) = 3^x$
2. $g(x) = \left(\frac{1}{3}\right)^x$

These are exponential functions with different bases.

Explanation of Each Function:

1. $f(x) = 3^x$:

   • This is an exponential growth function because the base, $3$, is greater than 1.
   • As $x$ increases, $f(x)$ grows rapidly.

2. $g(x) = \left(\frac{1}{3}\right)^x$:

   • This is an exponential decay function because the base, $\frac{1}{3}$, is between 0 and 1.
   • As $x$ increases, $g(x)$ decreases, approaching zero.

If you'd like, I can calculate specific values, compare these functions, or explain their properties further.

Would you like more details or have any questions?

Related Questions:

1. What are the properties of exponential growth and decay functions?
2. How do the graphs of $f(x) = 3^x$ and $g(x) = \left(\frac{1}{3}\right)^x$ compare?
3. What is the effect of the base in exponential functions on their behavior?
4. How would these functions behave as $x \to -\infty$ and $x \to +\infty$?
5. What transformations can be applied to these functions, and how do they affect their graphs?

Tip:

For exponential functions $a^x$ where $a > 1$, the function represents growth. For $0 < a < 1$, it represents decay.