1. The problem is to understand the behavior of a function as the input approaches negative infinity. 2. When analyzing limits at negative infinity, we look at the value of the function as $x \to -\infty$. 3. For example, consider a function $f(x) = ax^n + \dots$ where $a$ is the leading coefficient and $n$ is the highest power. 4. If $n$ is even and $a > 0$, then $f(x) \to +\infty$ as $x \to -\infty$. 5. If $n$ is even and $a < 0$, then $f(x) \to -\infty$ as $x \to -\infty$. 6. If $n$ is odd and $a > 0$, then $f(x) \to -\infty$ as $x \to -\infty$. 7. If $n$ is odd and $a < 0$, then $f(x) \to +\infty$ as $x \to -\infty$. 8. For rational functions, divide numerator and denominator by the highest power of $x$ in the denominator and analyze the limit. 9. For exponential functions like $f(x) = a^x$ with $a > 1$, $f(x) \to 0$ as $x \to -\infty$. 10. This approach helps predict end behavior of functions at negative infinity.