Mrs. Fleming is putting a tile backsplash on the wall behind her stove. The function f(x) gives how many boxes of tiles she would need if she used square tiles that are x inches per side.

Question

Mrs. Fleming is putting a tile backsplash on the wall behind her stove. The function f(x) gives how many boxes of tiles she would need if she used square tiles that are x inches per side.
What does f(4)<f(2) tell you?

GPT-4o mini · Answer

The notation $ f(4) < f(2) $ indicates that the number of boxes of tiles needed when using square tiles that are 4 inches per side is less than the number of boxes needed when using square tiles that are 2 inches per side. To understand this in practical terms, we can consider the following: 1. **Tile Area**: The area of a square tile is given by $ \text{Area} = x^2 $. Therefore: - A tile that is 4 inches per side has an area of $ 4^2 = 16 $ square inches. - A tile that is 2 inches per side has an area of $ 2^2 = 4 $ square inches. 2. **Coverage with Tiles**: When using larger tiles (4 inches by 4 inches), each tile covers more area compared to the smaller tiles (2 inches by 2 inches). Consequently, fewer tiles are needed to cover the same wall area. 3. **Conclusion**: Since $ f(4) < f(2) $, we conclude that using larger tiles (4 inches) requires fewer boxes of tiles than using smaller tiles (2 inches). This means that opting for larger tiles might be more efficient and less costly when it comes to covering the wall with the tile backsplash.