Find the domain and the range of the function. \( f(x)=\left\{\begin{array}{ll}-\frac{5}{7} x+3, & \text { for } x<7 \text {, } \\ -2, \quad \text { for } x \geq 7\end{array}\right. \) What is the domain of the given function? (Type your answer in interval notation.)

The domain of the function \( f(x) \) is all real numbers since there are no restrictions on the values of \( x \). In interval notation, it can be expressed as \( (-\infty, \infty) \). As for the range, the linear part of the function \( -\frac{5}{7} x + 3 \) decreases without bound as \( x \) approaches \( 7 \). When \( x = 7 \), the function's value is \( -2 \). Thus, the function takes all values from \(-\infty\) up to and including \(-2\) with the constant part at \(-2\) for \( x \geq 7\). Therefore, the range can be written in interval notation as \( (-\infty, -2] \).