To determine which table represents \( y = f(-x) \), we need to understand how the function transforms when we replace \( x \) with \( -x \). This transformation reflects the graph of the original function \( y = f(x) \) across the y-axis.
Given the potential values of \( f(-x) \) from the options, let's analyze what the values should resemble based on the original graph of the parabola. Here's a step-by-step guide to solving this:
- Reflect x-values: For positive \( x \), find corresponding negative \( x \) values (i.e., if \( f(x) = k \), then \( f(-x) \) at the mirrored x-value should also be \( k \)).
- Identify values in the graph: You need to check each table option to find whether they reflect within the limits set by the values on the original graph.
Since I cannot see the image or the original function graph, I cannot tell you exactly what the values of \( f(-x) \) would be. However, you can follow this approach:
- Identify what \( f(x) \) is for \( x = 1, 2, 3 \) in your drawing (the values of the original parabola).
- Use those values to find \( f(-1) \), \( f(-2) \), and \( f(-3) \).
- Compare the calculated values to the tables provided to find a match.
In essence, you are looking for a table that swaps the outputs for the positive x-values with the respective negative x-values while keeping symmetry about the y-axis.
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