The given function is:

\[
g(x) = e^{x+2} - 1
\]

### Key Insights about this function:
1. **Exponential Form**: The expression \(e^{x+2}\) is an exponential function. The base \(e\) is approximately 2.718, and it grows exponentially as \(x\) increases.
2. **Translation**: The function has been shifted horizontally by 2 units to the left due to the term \(x + 2\) inside the exponent. Additionally, the subtraction of 1 shifts the graph downward by 1 unit.

Would you like help with any specific operations related to this function, such as finding its derivative, integral, or evaluating it at specific points?

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### Related Questions:
1. What is the derivative of \(g(x)\)?
2. What happens to the function \(g(x)\) as \(x \to \infty\)?
3. How do you find the inverse of the function \(g(x)\)?
4. How would you graph \(g(x)\) using key points and transformations?
5. How do you integrate this function \(g(x)\)?

**Tip**: When dealing with exponential functions, remember that transformations such as shifts inside the exponent affect the graph in a way similar to how they would affect polynomials, but the growth remains exponentially fast.

Explore the exponential function g(x) = e^(x+2) - 1, which involves shifts and transformations. Learn about horizontal and vertical translations, how the exponential function behaves as x increases, and more. This content is ideal for advanced students in Grades 11-12.

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