The function you're dealing with is:

$f(x) = \frac{\sqrt[3]{x}}{x - 3}$

This function consists of two components:

1. The cube root of $x$, written as $\sqrt[3]{x}$ or $x^{1/3}$.
2. The denominator $x - 3$, which introduces a potential issue if $x = 3$ because it would make the denominator zero.

Important points:

• Domain: The domain is all real numbers except $x = 3$, where the denominator is zero and the function is undefined.
• Continuity: The function is continuous everywhere except at $x = 3$.
• Asymptote: Since the denominator goes to zero as $x$ approaches 3, there is a vertical asymptote at $x = 3$.

Would you like further details on graphing this function, analyzing its asymptotes, or differentiating it?

Follow-up questions:

1. What is the domain and range of $f(x)$?
2. How do you find the vertical asymptote of $f(x)$?
3. Can you find the critical points of $f(x)$ using derivatives?
4. How does the function behave near the vertical asymptote at $x = 3$?
5. Can you determine any local extrema for $f(x)$?

Tip:

When working with rational functions, always check for points where the denominator might become zero, as these are where vertical asymptotes may occur.