To help AS-Level math students recognize functions from their graphs, here are some simple steps to follow:

1. Vertical Line Test: A graph shows a function if you can draw a vertical line through it and it only touches the graph at one point. This means that for each input (or x-value), there is just one output (or y-value).

2. Types of Functions:

   • Linear Functions: These are represented by straight lines. They look like this: $y = mx + c$, where $m$ shows the slope (how steep the line is) and $c$ is where the line crosses the y-axis.
   • Quadratic Functions: These graphs form a U-shape called a parabola. They are usually written as $y = ax^2 + bx + c$, with $a$ not being zero.
   • Exponential and Logarithmic Functions: These graphs have unique curves that show quick growth or decrease.

3. Symmetry: Some graphs are symmetric, which can show what kind of function they are:

   • Even Functions: These are symmetric around the y-axis. An example is $y = x^2$.
   • Odd Functions: These are symmetric around the origin. A good example is $y = x^3$.

By using these tips, students can feel more confident in figuring out what type of function a graph represents!