Supply a valid technology formula for the given function.
4e^(1 + x)/x

The given function is:

\[
f(x) = 4 \frac{e^{1 + x}}{x}
\]

To express this in a more standard form, let's rewrite it clearly:

\[
f(x) = \frac{4e \cdot e^x}{x} = \frac{4e \cdot e^x}{x}
\]

This is a valid representation of the technology formula of the function.

### Domain Analysis
It's important to note that the domain of this function is all real numbers \( x \neq 0 \), since division by zero is undefined.

### Characteristics of the Function
- The numerator \( 4e \cdot e^x \) grows exponentially as \( x \to \infty \).
- The denominator \( x \) means that the overall function has an asymptote at \( x = 0 \).

Would you like a detailed analysis or graph of this function?

### Here are 5 Related Questions:
1. What is the derivative of \( f(x) = \frac{4e^{1 + x}}{x} \)?
2. How does \( f(x) \) behave as \( x \to \infty \) and \( x \to -\infty \)?
3. What is the integral of \( f(x) = \frac{4e^{1 + x}}{x} \)?
4. Are there any inflection points in the function \( f(x) \)?
5. How does the function change if \( 4e \) is replaced by a different constant?

### Tip
When dealing with exponential functions, always check the growth rate and compare it with polynomial terms in the denominator for asymptotic analysis.

Supply a valid technology formula for the given function: 4e^(1 + x)/x

Explore the exponential function f(x) = 4e^(1 + x)/x, including its domain, asymptotic behavior, and exponential growth properties. This detailed explanation is ideal for students in Grades 11-12 studying advanced functions and calculus.

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