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.