- The range of a function is defined as the set of all possible output values (y-values).
- By extracting the y-values from the provided table, we find the set \(\{9, 0, -7, -1\}\).
- Sorting these values in ascending order gives \(\{-7, -1, 0, 9\}\).
- Thus, the correct range is \(\boxed{\{y \mid y = -7, -1, 0, 9\}}\).
Explanation
- Understanding the Range of a Function
The range of a function is the set of all possible output values, which correspond to the values in the y-column of the given table. By inspecting the table provided:
\begin{center}
| \(x\) | \(y\) \) -5 | 9 \) 1 | 0 \) 4 | -7 \) 6 | -1 \) |
\end{center}
We can extract the y-values, which are \(9, 0, -7,\) and \(-1\). These constitute the range of the function.
- Determining the Range
To clearly express the range in set notation, we gather all unique y-values identified in the previous step: \(\{9, 0, -7, -1\}\). Sorting these values in ascending order, we obtain \(\{-7, -1, 0, 9\}\). Comparing this result to the given options, it corresponds to the set \(\{y \mid y = -7, -1, 0, 9\}\).
Examples
Understanding domains and ranges is essential in fields like data analysis and engineering. For example, if you are modeling the temperature of a machine over time, the 'domain' would be the set of time intervals recorded, and the 'range' would be the set of all observed temperatures. Correctly identifying these sets helps scientists and engineers define the bounds within which their systems operate, ensuring safe and efficient performance.