\( 1 \leftarrow \) The function \( f \) is defined as follows. Complete parts (a) to (d) below. \( f(x)=\left\{\begin{array}{ll}x+6 & \text { if }-4 \leq x<1 \\ 8 & \text { if } x=1 \\ -x+3 & \text { if } x>1\end{array}\right. \) (a) Find the domain of the function. The domain of the function \( f \) is (Type your answer in interval notation.)

The function \( f(x) \) is defined for three different cases, which gives us insight into its domain. The first case, \( -4 \leq x < 1 \), corresponds to the interval \([-4, 1)\). The second case, \( x = 1 \), adds the single point 1 to the domain. Finally, the third case, \( x > 1 \), corresponds to the interval \( (1, \infty) \). By combining these intervals, we find that the domain of the function \( f \) is: \[ [-4, \infty) \] This captures all values from \(-4\) to \(\infty\), including \(-4\) and \(1\), but not including numbers below \(-4\) or \(1\).