Ohio Assessments for Educators (OAE) Mathematics Practice Exam

When subtracting a constant k from the function f(x), this results in what type of shift?

1. Horizontal shift left

2. Vertical shift up

3. Vertical shift down

4. Horizontal shift right

The correct answer is: Vertical shift down

Subtracting a constant \( k \) from the function \( f(x) \) yields the new function \( f(x) - k \). This transformation affects the graph of the function vertically. Specifically, when you subtract a positive constant, each point on the graph of the original function decreases by \( k \) units in the vertical direction. Hence, the entire graph shifts downward by \( k \) units. This type of transformation maintains the same x-coordinates but changes the y-coordinates, leading to a vertical shift down. It is an essential concept in understanding function transformations, as vertical adjustments to functions directly impact their output values but do not modify their inputs or horizontal positioning. Thus, the correct understanding of this transformation is crucial for interpreting function behavior and graphing effectively.