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

The domain of the function \( f(x) \) is all real numbers, so in interval notation, it's expressed as \( (-\infty, \infty) \). This is because the function is defined for every \( x \) whether it is less than or greater than or equal to 7. As for the range, \( f(x) \) takes values according to two cases. For \( x < 7 \), as \( x \) approaches 7 from the left, \( f(x) \) approaches \( -\frac{5}{7} \times 7 + 3 = -\frac{35}{7} + 3 = -5 + 3 = -2 \). Therefore, from the left, \( f(x) \) can reach up to \( -2 \) but not including it. For \( x \geq 7 \), \( f(x) \) is constantly \( -2 \). Hence, the range in interval notation is \( (-\infty, -2] \).