d) \( g(x)=\left\{\begin{array}{ll}x+4, & -3 \leq x \leq-1 \\ x-4 & 1 \leq x \leq 3\end{array}\right. \)

The function \( g(x) \) is defined piecewise for two intervals. Let's break it down: 1. For the interval \( -3 \leq x \leq -1 \): \[ g(x) = x + 4 \] 2. For the interval \( 1 \leq x \leq 3 \): \[ g(x) = x - 4 \] The function is not defined for \( -1 < x < 1 \). ### Evaluating \( g(x) \) - For \( x = -3 \): \[ g(-3) = -3 + 4 = 1 \] - For \( x = -2 \): \[ g(-2) = -2 + 4 = 2 \] - For \( x = -1 \): \[ g(-1) = -1 + 4 = 3 \] - For \( x = 1 \): \[ g(1) = 1 - 4 = -3 \] - For \( x = 2 \): \[ g(2) = 2 - 4 = -2 \] - For \( x = 3 \): \[ g(3) = 3 - 4 = -1 \] ### Summary of Values - \( g(-3) = 1 \) - \( g(-2) = 2 \) - \( g(-1) = 3 \) - \( g(1) = -3 \) - \( g(2) = -2 \) - \( g(3) = -1 \) ### Graphing \( g(x) \) To graph \( g(x) \): - Plot the line segment from \( (-3, 1) \) to \( (-1, 3) \) for \( g(x) = x + 4 \). - Plot the line segment from \( (1, -3) \) to \( (3, -1) \) for \( g(x) = x - 4 \). - There will be no points plotted between \( -1 \) and \( 1 \) since \( g(x) \) is not defined in that interval. If you have any specific questions or need further analysis on this function, feel free to ask!