The function $f(x) = \ln(x+2)$ has a domain of $x > -2$, since the natural logarithm requires a positive argument.

To find the x-intercept of the graph of $f(x)$, we set $f(x) = 0$ and solve for $x$:

$\ln(x+2) = 0$

Recall that $\ln(1) = 0$. Therefore, we have:

$x + 2 = 1$

Solving for $x$:

$x = 1 - 2 = -1$

Thus, the x-intercept of the graph of $f(x)$ is at $x = -1$.

Do you want more details or have any questions?

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Here are 5 related questions for further exploration:

1. What is the domain and range of $f(x) = \ln(x+2)$?
2. How do we find the y-intercept of a function, and does $f(x)$ have one?
3. What is the derivative of $f(x) = \ln(x+2)$, and what does it tell us about the slope of the curve?
4. How does the transformation $f(x) = \ln(x+2)$ compare to the parent function $f(x) = \ln(x)$?
5. What is the vertical asymptote of the function $f(x)$, and how can we find it?

Tip:

For logarithmic functions, the argument inside the logarithm must always be positive, which defines the domain of the function.