Which of the following options best represents the range of the function?[-1, ∞)(-∞, -1](-∞, ∞)(-∞, 1]

To determine which option best represents the range of a function, we need to understand what the range encompasses. The range of a function is the set of possible output values (y-values) that it can produce based on its input (x-values).

1. Understanding the notations:

   • $[-1, ∞)$: This indicates that the function can take values from -1 to infinity, including -1.
   • $(-∞, -1]$: This indicates that the function can take values from negative infinity up to -1, including -1.
   • $(-∞, ∞)$: This indicates that the function can take any real number value.
   • $(-∞, 1]$: This indicates that the function can take values from negative infinity up to 1, including 1.

2. Analyzing the function: Without knowing the specific function, we can't definitively say which range applies. However, we can infer general properties:

   • If a function has a minimum value at -1 (like $f(x) = x^2 - 1$), its range would be $[-1, ∞)$.
   • If a function is bounded above by -1 (like $f(x) = -x - 1$), its range could be $(-∞, -1]$.

3. Conclusion: Given that many polynomial functions can have their ranges span either $[-1, ∞)$ or $(-∞, ∞)$. However, if we assume we're looking for a function that does not exceed a certain bound and has a minimum point (like the first option describes), then $[-1, ∞)$ might represent a common choice for specific types of functions.

Thus, without more context about the function, if your function reveals it doesn't output values less than -1, the best representation of the range would typically be:

Final Answer

$[-1, ∞)$