Transformations can really change how we look at sine, cosine, and tangent graphs! Let's break down the main effects in a simple way:

1. Vertical Shifts: When you add or subtract a number to the function, like in the example $y = \sin(x) + 2$, it moves the graph up or down. This means the center line of the graph shifts, which affects where the highest points (peaks) and lowest points (troughs) are.

2. Horizontal Shifts: If you add or subtract a number inside the function, like in $y = \sin(x - \frac{\pi}{2})$, the graph moves left or right. This changes where the peaks and points where the graph crosses zero appear, but it doesn't change the shape of the graph.

3. Amplitude Changes: When you multiply the function by a number, it stretches or squishes the graph up and down. For example, $y = 2\sin(x)$ makes the peaks twice as high, while $y = 0.5\sin(x)$ lowers them.

4. Period Changes: To change how often the graph goes up and down, you change the number in front of $x$. For instance, in $y = \sin(2x)$, the graph completes its wave faster, giving it a shorter period of $\frac{2\pi}{2} = \pi$.

These transformations help us understand how different trigonometric functions work, making graphing much more fun and exciting!