Determine which one of these graphs does not represent $y$ as a function of $x$ - AQA - A-Level Maths Mechanics - Question 3 - 2020 - Paper 3

To determine which graph does not represent $y$ as a function of $x$, we can apply the vertical line test. This test states that for a curve to be a function, any vertical line drawn must intersect the graph at most once.

1. Examine the first graph: This graph is a semi-circle, which passes the vertical line test since each vertical line intersects it at most once.
2. Examine the second graph: This graph is a line, which also passes the vertical line test.
3. Examine the third graph: This graph represents a standard function with a continuous curve, passing the vertical line test.
4. Examine the fourth graph: This graph has a part that could intersect a vertical line at two points, indicating it does not represent a function.

Therefore, the correct answer is to tick the box corresponding to the fourth graph.