Today I read the first section of the first chapter of my calculus book and worked on the associated exercises. (Yippee!) My concentration, which was such a problem on Thursday, was fine today, and I’m feeling encouraged.
The section I read was about functions and discussed the vertical line test. According to the test, a graph represents a function of $x$ if and only if no vertical line intersects the graph more than once. The way I remember first being taught the test, though, the “of $x$” condition was not included. It always bothered me that $y=x^2$, an upward facing parabola, should be a function, while $x=y^2$, a rightward facing parabola, should not. It is, of course. It’s just a function of $y$ rather than a function of $x$. This has me wondering whether, say, the graph of a diagonally facing parabola could be interpreted as representing a function, and what it would be a function of.1
- To do. ↩︎