Transformations of functions can show us symmetry (where things are balanced) and asymmetry (where things are not balanced) in graphs in the following ways:

1. Translations: This means moving a graph sideways or up and down. When you shift a graph, it keeps its symmetry. For example, if you change the function to $f(x) \rightarrow f(x - h)$, it moves the graph to the right if $h$ is a positive number (more than 0) and to the left if $h$ is a negative number (less than 0).

2. Reflections: This happens when you flip a graph over the $x$-axis (the horizontal line) or the $y$-axis (the vertical line). For example, flipping over the $x$-axis looks like this: $f(x) \rightarrow -f(x)$. Flipping over the $y$-axis looks like this: $f(x) \rightarrow f(-x)$. Both of these actions can create or keep symmetry in the graph.

3. Stretching & Compressing: This is about changing the size of the graph. When you stretch it up and down (like $f(x) \rightarrow kf(x)$ where $k$ is more than 1), it can make things look uneven or asymmetrical. But if you stretch it side to side (like $f(x) \rightarrow f(\frac{x}{k})$ where $k$ is more than 1), it can keep symmetry for some special functions, like even functions.

These changes help us look at how functions behave, especially when it comes to symmetry. For example, even functions, like $f(x) = x^2$, are symmetrical around the $y$-axis. On the other hand, odd functions, like $f(x) = x^3$, are symmetrical around the origin (the point where the two axes meet).

Understanding these ideas is important for studying functions in pre-calculus.