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.)

To find the domain and range of the given function \( f(x) \), we need to consider the two cases defined by the function: 1. For \( x < 7 \), the function is defined as \( f(x) = -\frac{5}{7}x + 3 \). 2. For \( x \geq 7 \), the function is defined as \( f(x) = -2 \). ### Domain: The domain of a function is the set of all possible input values for which the function is defined. In this case, the function is defined for all real numbers, so the domain is \( (-\infty, \infty) \). ### Range: The range of a function is the set of all possible output values for which the function is defined. To find the range, we need to consider the two cases: 1. For \( x < 7 \), the function is \( f(x) = -\frac{5}{7}x + 3 \). This is a linear function, and its range is all real numbers. 2. For \( x \geq 7 \), the function is \( f(x) = -2 \). This is a constant function, and its range is a single value, \( -2 \). Therefore, the range of the function is \( (-\infty, -2] \). So, the domain of the given function is \( (-\infty, \infty) \) and the range is \( (-\infty, -2] \).