\( f(x)=\left\{\begin{array}{ll}x+6 & \text { if }-4 \leq x<1 \\ 8 & \text { if } x=1 \\ -x+3 & \text { if } x>1\end{array}\right. \) (a) Find the domain of the function. The domain of the function \( f \) is \( [-4, \infty) \). (Type your answer in interval notation.) (b) Locate any intercepts. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The intercept(s) is/are (Type an ordered pair. Use a comma to separate answers as needed.) B. There are no intercepts.

The function \( f(x) \) is defined for all \( x \) where \( -4 \leq x < 1 \) and \( x > 1 \). This means the domain covers all real numbers from -4 to infinity, represented as \( [-4, \infty) \). To find the intercepts, we check where the function crosses the axes. For the x-intercept, set \( f(x) = 0 \) and solve: 1. In the segment \( x + 6 = 0 \) leads to \( x = -6 \) but this is outside the domain. 2. In the segment \( -x + 3 = 0 \) leads to \( x = 3 \), which is in the domain, giving the x-intercept at (3, 0). The y-intercept is found with \( f(0) = 0 + 6 = 6 \), so it is at (0, 6). Therefore, the intercepts are at (3, 0) and (0, 6). So, A. The intercepts are (3, 0), (0, 6).