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.