You have the function:

\[
f(x) = \frac{5}{49 + x^2}
\]

This is a rational function, with \( f(x) \) defined as a ratio of constants and a quadratic expression in \(x\). Let's explore the properties of this function:

### 1. **Domain**:
The denominator \( 49 + x^2 \) is never zero since \( x^2 \geq 0 \) for all real \(x\), and thus \( 49 + x^2 \geq 49 \). Therefore, the domain is all real numbers:

\[
\text{Domain: } (-\infty, \infty)
\]

### 2. **Range**:
The function has a minimum value at \( x = 0 \), where:

\[
f(0) = \frac{5}{49 + 0^2} = \frac{5}{49}
\]

As \( x \to \infty \) or \( x \to -\infty \

Explore the properties of the rational function f(x) = 5 / (49 + x^2), including domain, range, and behavior. This problem covers key concepts such as rational functions and quadratic expressions, making it ideal for students in Grades 10-12.

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