Ohio Assessments for Educators (OAE) Mathematics Practice Exam

What happens to the graph of f(x) when it is multiplied by a whole number k?

1. Reflected over the x-axis

2. Vertically compressed

3. Only horizontally stretched

4. Vertically stretched

The correct answer is: Vertically stretched

When a function \( f(x) \) is multiplied by a whole number \( k \) (where \( k > 1 \)), the graph of the function undergoes a vertical stretch. This transformation effectively means that for every point on the graph of the original function, the y-coordinates are multiplied by \( k \). As a result, if the original function \( f(x) \) has a certain value at a specific \( x \), the new function \( k \cdot f(x) \) will have a larger value at that same \( x \), causing the points of the graph to move further away from the x-axis. For example, if \( k = 2 \), every y-value of the graph is doubled, making the peaks higher and the valleys deeper, thus stretching the graph vertically. The transformation does not affect the shape of the graph horizontally or its overall orientation related to the x-axis. In contrast, a multiplier less than one (but greater than zero) would compress the graph vertically, bringing points closer to the x-axis. Therefore, understanding the effect of multiplying the function by different values is crucial for analyzing how the graph of the function transforms.