Transformations of functions change how their graphs look and where they’re located. In Year 11 Math, students learn about four main types of transformations: translations, reflections, stretches, and compressions.

1. Translations:

   • A horizontal translation happens with the equation (f(x - a)). This means if (a > 0), the graph moves (a) units to the right. If (a < 0), it moves (a) units to the left.
   • A vertical translation is shown by (f(x) + b). Here, if (b > 0), the graph moves (b) units up, and if (b < 0), it moves (b) units down.

2. Reflections:

   • To reflect a graph across the x-axis, we use (-f(x)). For a reflection across the y-axis, we use (f(-x)).

3. Stretches and Compressions:

   • A vertical stretch or compression is done with (k \cdot f(x)). If (k > 1), it stretches the graph up and down. If (0 < k < 1), it compresses the graph.
   • A horizontal stretch or compression is explained by (f(\frac{x}{k})). If (k > 1), it compresses the graph left and right. If (0 < k < 1), it stretches the graph.

Knowing these transformations helps students draw graphs from equations better. It gives them a clearer picture of how changing a function affects its graph, which is useful for solving real-world problems.