The First Article to Read

First two plots of the identity function $y=x$. The numbers we'll be using are the real numbers:

The plots and figures are in an aspect ratio 2:1 canvas, which is a squat rectangle.

An interval here means two different real numbers, symbolically $a$ and $b$, along with everything in between, using square brackets it's written like so: $[a, b]$.


A plot of the identity function, on the interval $[1, 3]$. There is also a highlight at the point $y=x=1.9$.


A plot of the identity function, on the interval $[0, 2]$.

The highlight point at $1.9$ appears different in the two plots because the intervals are different. If this was an interesting function, anything other than the identity, it would have some curvature, and this curvature will be accentuated or attenuated by the interval of the abscissa.

The ordinate and the abscissa are also known as y and x coordinates, or axes. The ordinate is the "vertical" axis, which is the bottom-to-top scale of the plots. The ordinate will go from the minimum value of $f(x)=y$ to the maximum of the curve, with the average of the two going in the middle vertical indicator. $x$ is the variable in the function, and goes on the "horizontal" axis. So, in the plots, it's the function value as indicated by going straight up from a point on the abscissa (an $x$ value) to the curve, and the height is as indicated on the left axis.

A line, such as $y=x$, has no width, and since the eye can't percieve that, lines are stroked, dashed, and colored to make them visible and distinguishable.

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