What happens when you change the graph of f(x) to f(−x) ?(1 point) Responses The graph is reflected across the y-axis. The graph is reflected across the y-axis. The line is reflected across the x-axis. The line is reflected across the x-axis. The graph is moved 1 unit to the left. The graph is moved 1 unit to the left. The graph is moved 1 unit down.
The correct answer is: The graph is reflected across the y-axis.
When you change the graph of f(x) to f(−x), the graph is reflected across the y-axis. This means that every point on the original graph will have its x-coordinate negated, resulting in a mirror image of the graph on the opposite side of the y-axis.
When you change the graph of f(x) to f(-x), there are a few changes that occur:
1. Reflection across the y-axis: The graph is symmetric with respect to the y-axis, meaning that if you were to fold the graph along the y-axis, the two sides would overlap perfectly.
2. Reflection across the x-axis: This statement is incorrect. Changing the input from x to -x does not reflect the graph across the x-axis. Instead, it reflects across the y-axis.
3. Movement to the left: This statement is incorrect. Changing the input from x to -x does not move the graph to the left. It simply reflects the graph across the y-axis.
4. Movement down: This statement is incorrect. Changing the input from x to -x does not move the graph down. It only reflects the graph across the y-axis.
In summary, when you change the graph of f(x) to f(-x), the graph is reflected across the y-axis.