The given function is $p(x) = x^3 - 10x^2 - 4$. We are asked to determine the behavior of $p(x)$ as $x$ decreases without bound, i.e., as $x \to -\infty$.

Step-by-step analysis:

1. Highest Degree Term (Dominant Term): The term with the highest power of $x$ is $x^3$, which dominates the behavior of the function for large values of $|x|$. Specifically, for large negative values of $x$, $x^3$ becomes very negative since $(-x)^3 = -x^3$ for negative $x$.

2. Other Terms:

   • The $-10x^2$ term grows positively (since $x^2$ is always positive), but this term is not as strong as $x^3$ for large negative $x$.
   • The constant term $-4$ is negligible compared to the dominant $x^3$ term as $x \to -\infty$.

Conclusion:

As $x \to -\infty$, the cubic term $x^3$ dominates and drives the function $p(x)$ to decrease without bound. Therefore, the correct answer is:

A. The output values decrease without bound.

Would you like further explanation or more details?

Here are 5 related questions to deepen your understanding:

1. How would the behavior of $p(x)$ change if the leading term was $-x^3$?
2. How does the behavior of the function change as $x \to +\infty$?
3. What effect does the $-10x^2$ term have on the behavior of the function at different ranges of $x$?
4. How would the function behave if the cubic term was absent?
5. Can you graph $p(x) = x^3 - 10x^2 - 4$ and describe its key features (such as intercepts and turning points)?

Tip: For polynomial functions, always focus on the highest degree term when analyzing behavior as $x \to \infty$ or $x \to -\infty$.