came across this function … with the value r being a variable
Hi Ben. Here's some information about terminology. The relationship between your x and y is not a
function, and r is not called a variable (even though its value may vary).
If y were a function of x, then there would be only one output (y-value) for any valid input (x-value). As explained in the 'function' link above, any vertical, intersecting line drawn on a
function's graph must touch the curve at one point only. If such a line contacts the graph more than once, then there are two or more outputs for that value of x — violating the definition of a function.
Symbol r represents a
parameter. Parameters are fixed values (constants) that change from one application or equation to another within the same family. For example, the equation of a non-vertical line in the xy-plane (written in Slope-Intercept form) is [imath]y=mx+b[/imath]. Symbols x and y are variables; symbols m and b are parameters. So, m and b are fixed for any particular line in the family of such lines, but whenever we switch to a different line, the parameter values m and b change.
sorry about all the pictures
There's no need for sorrow! We really like pictures, and 'more' is generally better than 'less'. Cheers
[imath]\;[/imath]
