Ohio Assessments for Educators (OAE) Mathematics Practice Exam

If k is negative in the expression f(k×x), what effect does it have on the function?

1. It reflects the function across the y-axis

2. It stretches the function vertically

3. It has no effect on the function

4. It compresses the function horizontally

The correct answer is: It reflects the function across the y-axis

In the expression f(k × x), when k is negative, it has the effect of reflecting the function across the y-axis. This occurs because the multiplication by a negative value changes the sign of the input variable x, effectively flipping the function's output for positive x-values to become corresponding negative outputs and vice versa. For instance, if you consider the function f(x) and how it behaves under the transformation f(-x), every point on the graph of f(x) for positive x-values is mirrored onto the corresponding negative x-values, while points on the graph for negative x-values mirror to positive x-values. This reflection leads to a change in the visual representation of the graph, making it appear flipped around the y-axis. The other options do not accurately describe the effects of a negative k in this context, focusing instead on vertical stretches or compressions, which occur due to changes in the function's output rather than the input. Moreover, saying there is no effect does not account for the significant transformation made by the function's reflection across the y-axis.