- Scan the provided table for the value \(-3\) in the \(f(x)\) column.
- Identify the corresponding \(x\) value in the same row.
- Conclude that for \(f(x) = -3\), \(x\) must be \(-1\).
- Final answer: \(\boxed{-1}\).
Explanation
- Analyzing the Data and Objective
We are given a function \(f(x)\) represented by a table of values. Our objective is to determine the input value \(x\) such that the output value \(f(x)\) is \(-3\). The provided table lists the relationships between various inputs \(x\) and their corresponding outputs \(f(x)\):
\[ \begin{array}{|l|l|} \ x & f(x) \\ -4 & -66 \\ -3 & -29 \\ -2 & -10 \\ -1 & -3 \\ 0 & -2 \\ 1 & -1 \\ 2 & 6 \\ \end{array} \]
- Locating the Function Value in the Table
To find the value of \(x\) for which \(f(x) = -3\), we search the "f(x)" column in the provided table for the value \(-3\). Scanning the column, we locate the row where \(f(x) = -3\), which corresponds to the fourth row.
- Identifying the Value of \(x\) and Conclusion
In the row where \(f(x) = -3\), we look at the "x" column to determine the corresponding input value. The table shows that when \(f(x) = -3\), the value of \(x\) is \(-1\). Thus, comparing this with the provided choices: -29, -10, -3, and -1, we find that the correct choice is -1.
Examples
Tables like the one provided are frequently used in scientific experiments and data analysis to show relationships between variables. For example, a biologist might record the growth height of a plant at different time intervals to observe its progress. By checking the table, one can easily identify the exact time at which the plant reached a specific height, similar to how we identified the input for a given output here. Understanding how to read data tables is a foundational skill in statistics and algebra for interpreting complex information efficiently.