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The given mathematical expression is:

\[
f(x) = \frac{3x}{x^2 + 5x + 6}
\]

This is classified as a **rational function** because it represents the ratio of two polynomials (the numerator \( 3x \) and the denominator \( x^2 + 5x + 6 \)). A rational function is defined as any function of the form \( \frac{P(x)}{Q(x)} \), where \( P(x) \) and \( Q(x) \) are polynomials and \( Q(x) \neq 0 \).

So, the correct answer is: **Rational Function**.

Would you like more details or have any questions?

Here are five related questions:
1. What are the vertical asymptotes of this rational function?
2. How do you determine the horizontal asymptote of this rational function?
3. Can you factor the denominator \( x^2 + 5x + 6 \)?
4. How do you find the domain of a rational function?
5. What are the zeros of the rational function?

**Tip:** When working with rational functions, always check for any restrictions on the domain by ensuring the denominator never equals zero.

What type of mathematical object is the function f(x) = 3x / (x^2 + 5x + 6)?

Explore how to classify rational functions like f(x) = 3x / (x^2 + 5x + 6), which is a ratio of polynomials. Learn how to determine its domain, asymptotes, and key properties. Suitable for Grades 9-12 students.

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