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 \( (-\infty, \infty) \). (Type your answer in interval notation.) The range of \( f(x) \) is \( \square \). (Type your answer in interval notation.)

We start with the basic cubic function, g(x) = x³, which has a domain of (–∞, ∞) and a range of (–∞, ∞). Now, consider the function:   f(x) = -(x + 1)³ – 4 Below are the step-by-step transformations: 1. Replace x by (x + 1) in x³.   • This shifts the graph 1 unit to the left.   • New graph: h(x) = (x + 1)³ 2. Multiply the function by –1.   • This reflects the graph across the x-axis.   • New graph: k(x) = –(x + 1)³ 3. Subtract 4 from the function.   • This shifts the graph 4 units downward.   • Final graph: f(x) = –(x + 1)³ – 4 Since cubic functions naturally extend in both vertical directions, these transformations do not restrict the function’s output. Therefore:  Domain of f(x): (–∞, ∞)  Range of f(x): (–∞, ∞) When using your graphing tool, you should see the basic cubic shape shifted, reflected, and translated according to the steps described.