If y = -f(x), what transformation occurs?

If y = -f(x), what transformation occurs?

• A. Movement left on the x axis
• B. Reflection in the y axis
• C. Movement down on the y axis
• D. Reflection in the x axis

Answer: (C)

To understand the transformation represented by the equation y = -f(x), we need to analyze what happens to the graph of f(x). This equation indicates that for every point on the graph of f(x), the y-coordinate is multiplied by -1. As a result, each point (x, f(x)) on the original graph is transformed to (x, -f(x)). This means that instead of points being located at their original height above the x-axis, they will now be positioned the same distance below the x-axis. This operation essentially "flips" the graph over the x-axis, creating a mirror image of the original graph in relation to the x-axis. Therefore, the correct transformation that occurs is a reflection in the x-axis. This transformation changes the sign of the output values for the function at all x-values, which is characteristic of reflecting a graph over the x-axis.

To understand the transformation represented by the equation y = -f(x), we need to analyze what happens to the graph of f(x). This equation indicates that for every point on the graph of f(x), the y-coordinate is multiplied by -1. As a result, each point (x, f(x)) on the original graph is transformed to (x, -f(x)).

This means that instead of points being located at their original height above the x-axis, they will now be positioned the same distance below the x-axis. This operation essentially "flips" the graph over the x-axis, creating a mirror image of the original graph in relation to the x-axis.

Therefore, the correct transformation that occurs is a reflection in the x-axis. This transformation changes the sign of the output values for the function at all x-values, which is characteristic of reflecting a graph over the x-axis.