When students learn about function notation, they sometimes make mistakes that can be confusing. Here are some common ones:

1. Mixing Up Function Notation and Multiplication: Many students think that $f(x)$ means $f$ times $x$. But really, $f(x)$ shows the result of the function $f$ when you put in $x$ as the input.

2. Forgetting About the Domain: Sometimes, students forget to think about the domain of the function. For example, in $f(x) = \frac{1}{x-2}$, the value of $x$ cannot be 2. If it is, the function doesn’t work.

3. Misunderstanding Function Values: Some students believe that $f(2) + f(3)$ means just adding the numbers 2 and 3 together. Instead, they need to first find out what $f(2)$ and $f(3)$ are before adding them.

By clearing up these mistakes, students can better understand function notation in algebra.