https://file.aiquickdraw.com/mathbot/file/17297393932364xlssixg.jpg

From the graph and the equations provided, we can match each function to its corresponding graph by considering the shape and behavior of these well-known functions.

Let's analyze the options:

1. **\( \ln(x) \)**:
   - The natural logarithm, \( \ln(x) \), is defined for positive \( x \) values, and the graph increases but flattens out as \( x \) grows. This matches the **green (G)** curve.
   
2. **\( e^x \)**:
   - The exponential function, \( e^x \), grows rapidly as \( x \) increases and approaches 0 as \( x \) becomes negative. This is consistent with the **red (R)** curve.
   
3. **\( 10^x \)**:
   - Similar to \( e^x \), \( 10^x \) also represents exponential growth, but it grows even faster than \( e^x \). The behavior is again increasing quickly as \( x \) grows and very close to 0 for negative \( x \). This is represented by the **black (K)** curve.
   
4. **\( \log(x) \)**:
   - The base-10 logarithm, \( \log(x) \), behaves similarly to \( \ln(x) \) but grows slower. It matches the **blue (B)** curve.

So, the correct matching is:

- **\( \ln(x) \) → Green (G)**
- **\( e^x \) → Red (R)**
- **\( 10^x \) → Black (K)**
- **\( \log(x) \) → Blue (B)**

Would you like any more details on these functions or their graphs? Here are five related questions:

1. What is the domain of \( \ln(x) \) and how does it differ from \( \log(x) \)?
2. How does the rate of growth of \( e^x \) compare to \( 10^x \)?
3. Why do logarithmic functions only exist for positive values of \( x \)?
4. How do base-10 logarithms differ from natural logarithms in practical applications?
5. What happens to \( e^x \) and \( 10^x \) as \( x \) approaches infinity?

**Tip**: Exponential functions (like \( e^x \) and \( 10^x \)) grow faster than polynomial or logarithmic functions as \( x \) increases.

Match each equation with a graph above: ln(x), e^x, 10^x, log(x).

Learn how to match logarithmic and exponential functions like ln(x), e^x, 10^x, and log(x) with their corresponding graphs. This exercise covers key mathematical concepts and graph behavior. Suitable for students in Grades 9-12.

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