Starting with the graph of a basic function, graph the following function using the techniques of shifting, compressing, stretching, and/or reflecting. Find the domain and range of the function. \( f(x)=-(x+1)^{3}-4 \) Use the graphing tool to graph the equation. The domain of \( f(x) \) is (Type your answer in interval notation.)

To graph the function \( f(x) = -(x+1)^3 - 4 \), start with the basic cubic function \( g(x) = x^3 \). First, shift the graph left by 1 unit to account for the \( (x+1) \) term. Next, reflect the graph across the x-axis due to the negative sign in front, resulting in \( h(x) = -(x+1)^3 \). Lastly, shift the entire graph down by 4 units for the final transformation. The domain of \( f(x) \) is all real numbers, which in interval notation is \( (-\infty, \infty) \). The range, considering the transformations, is all real numbers less than or equal to -4, written in interval notation as \( (-\infty, -4] \).