Question
What does the transformation f(x) -> f(-x) do to the graph?
Answers
GPT-4o mini
The transformation \( f(x) \to f(-x) \) reflects the graph of the function \( f(x) \) across the y-axis. This means that every point \( (x, f(x)) \) on the original graph will have a corresponding point \( (-x, f(-x)) \) on the transformed graph.
Here are a few key points to remember about this transformation:
1. **Even Functions**: If the original function \( f(x) \) is an even function (i.e., \( f(x) = f(-x) \)), then the graph will look the same before and after the transformation.
2. **Graph Behavior**: Points that were located on one side of the y-axis will find their corresponding points mirrored on the opposite side of the y-axis.
3. **Applications**: This transformation is useful in analyzing symmetry in functions. If a function has y-axis symmetry, applying the transformation will not change its appearance.
Overall, reflect the graph across the y-axis when applying the transformation \( f(x) \to f(-x) \).
Here are a few key points to remember about this transformation:
1. **Even Functions**: If the original function \( f(x) \) is an even function (i.e., \( f(x) = f(-x) \)), then the graph will look the same before and after the transformation.
2. **Graph Behavior**: Points that were located on one side of the y-axis will find their corresponding points mirrored on the opposite side of the y-axis.
3. **Applications**: This transformation is useful in analyzing symmetry in functions. If a function has y-axis symmetry, applying the transformation will not change its appearance.
Overall, reflect the graph across the y-axis when applying the transformation \( f(x) \to f(-x) \).