1. The problem is to understand the transformation of a function when its output changes from 2 to 4. 2. A vertical stretch by a scale factor $k$ means every $y$-value of the function is multiplied by $k$. 3. Since the output changes from 2 to 4, we find the scale factor by dividing the new output by the original output: $$k = \frac{4}{2} = 2$$ 4. This means the function is vertically stretched by a factor of 2. 5. In simple terms, the graph is pulled away from the x-axis, doubling the height of every point. 6. Therefore, the vertical stretch scale factor is 2.