To evaluate the function \( h(x) = \frac{3x}{x + 2} \) at \( x = 2 \), we need to substitute \( x = 2 \) into the function.

The function is:

\[ h(x) = \frac{3x}{x + 2} \]

Substitute \( x = 2 \):

\[ h(2) = \frac{3 \cdot 2}{2 + 2} \]

Simplify the expression:

\[ h(2) = \frac{6}{4} \]

Reduce the fraction:

\[ h(2) = \frac{3}{2} \]

So, \( h(2) = \frac{3}{2} \).

Would you like more details or have any questions?

Here are some related questions to expand your understanding:

1. What is the domain of the function \( h(x) = \frac{3x}{x + 2} \)?
2. How would you determine if \( h(x) \) has any vertical asymptotes?
3. What are the intercepts of the function \( h(x) \)?
4. How do you find the horizontal asymptote of the function \( h(x) \)?
5. Can \( h(x) = \frac{3x}{x + 2} \) be simplified further, and if so, how?
6. How would you graph the function \( h(x) = \frac{3x}{x + 2} \)?
7. What is the behavior of \( h(x) \) as \( x \) approaches infinity?
8. How do you find the inverse of the function \( h(x) \)?

**Tip:** When working with rational functions, always check for values that make the denominator zero, as these are points where the function is undefined.

Learn how to evaluate the rational function h(x) = 3x/(x + 2) at x = 2 step-by-step. This problem involves function evaluation, rational functions, and algebraic manipulation. Suitable for high school students in Grades 9-12.

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