https://file.aiquickdraw.com/mathbot/file/1730939861092oc7nw3rm.jpg

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.

Given the functions f(x) = 3^x and g(x) = (1/3)^x, analyze the behavior of these exponential functions.

Explore the properties of the exponential functions f(x) = 3^x and g(x) = (1/3)^x. Learn how exponential growth and decay differ and how these functions behave as x approaches positive and negative infinity.

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