Transformations can really change how a polynomial function looks on a graph. Understanding these changes helps us see functions in a new light!

1. Vertical Shifts:
   When you add or subtract a number from a polynomial, like turning $f(x)$ into $f(x) + k$, you are shifting the graph up or down.

• If $k$ is positive, the graph moves up.
• If $k$ is negative, the graph moves down.
  Imagine moving the whole graph up or down without changing its shape!

2. Horizontal Shifts:
   If you change the input by a number, like turning $f(x)$ into $f(x - h)$, the graph shifts left or right.

• A positive $h$ moves the graph to the right.
• A negative $h$ moves it to the left.

3. Stretching and Compressing:
   When you multiply the function by a number, like changing $f(x)$ to $af(x)$:

• If $|a| > 1$, the graph stretches vertically, making it taller.
• If $0 < |a| < 1$, it compresses, making the graph look squished.
  It’s all about how "tall" or "squished" the graph appears!

4. Reflection:
   Sometimes, the graph can flip depending on the sign you multiply with.
   For example, changing $f(x)$ to $-f(x)$ flips the graph over the x-axis.

These transformations help us change and explore polynomial functions in so many exciting ways!