Visualizing functions can make understanding the Fundamental Theorem of Calculus (FTC) harder instead of easier. Many students struggle with the abstract idea that the area under a curve connects to the total amount of area, which can lead to misunderstandings.

1. Understanding Area: The FTC connects two ideas: differentiation and integration. However, many students find it tough to see how the total area under a curve, represented by $f(x)$, connects with its derivative, $f'(x)$.

2. Reading Graphs: Sometimes, students misread the graphs. They don’t realize that the area function $F(x) = \int_{a}^{x} f(t) \, dt$ is linked to $f(x)$.

To help with these challenges, using interactive graphing tools or software can be very helpful. These tools let students play around with the graphs of $f(x)$ and $F(x)$. This hands-on experience can make the idea of area more clear and easier to understand.