As x approaches zero from the right, the magnitude of the rate of change of 1/x increases. This is why the frequency of the sine wave increases as one moves to the left in the graph.
In the branch of mathematics known as topology, the topologist's sine curve or Warsaw sine curve is a topological space with several interesting properties that make it an important textbook example.
![{\displaystyle T=\left\{\left(x,\sin {\tfrac {1}{x}}\right):x\in (0,1]\right\}\cup \{(0,0)\}.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7d4221bd712b70257f7e0f8d9b1ca74eaff5661c)