The First Article to Read

The numbers we'll be using are the real numbers:

Firstly, here are two plots of the identity function $y=x$, showing what a line with slope of unity looks like. It's called the identity function because it takes the parameter $x$ (at every point on the interval) and outputs the same number (identically). 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; by comparing the axes and noting that the highlighted point in both plots indicate the same point. If this was an interesting function, anything other than a line, it would have some curvature.

The ordinate and the abscissa are also known as $y$ and $x$ coordinates, or axes. The ordinate is the vertical axis, and reading a point on the plotted curve (lines in this article) means associating a point (below it) on the abscissa with a point on the ordinate axis, as the pair of numbers at the highlighted point indicate. The ordinate will go from the minimum value of the function (on the given interval) to the maximum of the curve, indicated as the upper and lower numbers on the vertical axis, so for the identity function the range of the ordinate is the same as the interval of the abscissa. In the plots the function value as indicated by going straight up from a point on the abscissa (an $x$ value in the interval of interest) to the curve (line in these plots), and the height (function value or magnitude) is as indicated on the left axis.

The plot is a visualization tool, not an exact or complete representation of the mathematical formula. A curve, such as this line $y=x$ being a formula with an argument/parameter $x$, has no mathematical 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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