Ohio Assessments for Educators (OAE) Mathematics Practice Exam 2025 - Free Practice Questions and Study Guide

In the context of the function \( f(x) \) when multiplied by a fraction \( k \), the resulting transformation affects the graph of the function in a specific manner. When \( k \) is a fraction, it represents a number less than 1 and greater than 0. This applies a vertical compression to the function.

Specifically, a vertical compression means that every point on the graph of the function is pulled closer to the x-axis. For example, if \( f(x) \) has a value of 2 at a certain point, then \( k \times f(x) \) will have a value that is a fraction of that, effectively making the output smaller. This is why the correct statement involves vertical compression: the effect of multiplying by a fraction reduces the height of the graph without changing its overall direction.

In contrast, a vertical stretch would occur if \( k \) were greater than 1, resulting in points moving away from the x-axis, while horizontal compression would relate to multiplying \( x \) by a fraction less than 1 inside the function. A reflection over the y-axis does not apply here since that transformation occurs when \( x \) is replaced with \(-x\) in the function.