Ohio Assessments for Educators (OAE) Mathematics Practice Exam

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Which statement is true when k is a fraction in the expression k×f(x)?

It leads to a vertical stretch
It results in horizontal compression
It causes a vertical compression
It reflects the function over the y-axis

The correct answer is: It causes a vertical compression

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.