Suppose that the function \( g \) is defined, for all real numbers, as follows. \[ g(x)=\left\{\begin{array}{cc}-3 & \text { if } x<-1 \\ 2 & \text { if } x=-1 \\ -1 & \text { if } x>-1\end{array}\right. \] Graph the function \( g \).

To graph the function \( g \), we need to consider the different cases outlined in its piecewise definition. 1. For \( x < -1 \), \( g(x) = -3 \). This means that for every number less than -1, the y-coordinate will be -3. We plot a horizontal line at \( y = -3 \) from far left until \( x = -1 \). 2. At \( x = -1 \), \( g(x) = 2 \). This is a single point, so we place a filled-in dot at the coordinate (-1, 2). 3. For \( x > -1 \), \( g(x) = -1 \). For every number greater than -1, the y-coordinate will be -1. We plot a horizontal line at \( y = -1 \) starting just to the right of \( x = -1 \) and extending to the right. In summary, the graph will have: - A horizontal line at \( y = -3 \) for \( x < -1 \). - A point at (-1, 2). - A horizontal line at \( y = -1 \) for \( x > -1 \). When plotted, the graph clearly demonstrates the piecewise behavior of the function \( g \).