Find the domain of the following rational function.
Upper R left parenthesis x right parenthesis equals StartFraction 16 x Over x plus 3 EndFraction

To find the domain of the rational function \( R(x) = \frac{16x}{x + 3} \), we need to determine where the function is defined. A rational function is undefined where its denominator is zero, since division by zero is not allowed.

### Steps:

1. **Identify the denominator**: The denominator of the function is \( x + 3 \).
2. **Set the denominator equal to zero**: Solve \( x + 3 = 0 \) to find the value of \( x \) where the function is undefined.
   \[
   x + 3 = 0
   \]
   \[
   x = -3
   \]
3. **Conclusion**: The function is undefined when \( x = -3 \). Therefore, the domain of the function is all real numbers except \( x = -3 \).

### Domain:
\[
\boxed{(-\infty, -3) \cup (-3, \infty)}
\]

This means that the function is defined for all real numbers except \( x = -3 \).

Do you have any questions or want further details on this?

Here are 5 related questions to explore:
1. What is the range of this rational function?
2. How do we find vertical asymptotes for rational functions?
3. What happens to the function \( R(x) \) as \( x \to -3 \)?
4. Can you determine the horizontal asymptote of the function \( R(x) \)?
5. How would the graph of \( R(x) = \frac{16x}{x + 3} \) look like?

**Tip**: For rational functions, always check the denominator for zero to find domain restrictions!

Find the domain of the following rational function. R(x) = \frac{16x}{x + 3}

Discover how to find the domain of the rational function R(x) = 16x/(x + 3) by analyzing where the function is undefined. Learn about rational functions, domain restrictions, and important algebraic concepts. Suitable for students in Grades 9-11.

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