The table object is what's commonly called a "lookup table" or an "array". You can store an ordered array of numbers, and then look up those numbers by referring to their "index" number (also sometimes called the "address") in the array. In table, the index numbers start from 0, and each location in the array can hold an integer. In the table's Inspector, you can set it to save its contents as part of the patch, so that the stored numbers will always be there the next time you open the patch.
The most direct way to convert one range of numbers into a different range of numbers is a process called linear mapping. For each number in a source (input) range, find the corresponding number in a destination (output) range. The process is to multiply the input value by the size of the destination range (destination maximum minus destination minimum) divided by the source range (source maximum minus source minimum), then add the destination minimum to that.
The function object can be used to create line segment functions that control a line~ object, and it can also be used as a lookup table. A number coming in its inlet will be treated as a point on the x-axis, and whatever y-axis value is shown on the line segment function at that point will be sent out the leftmost outlet. This example patch demonstrates that use of function.
Each MSP object (each object that has signal input and/or output) is always producing signal as long as audio is turned on. For example, signal generators like cycle~ (sinusoidal wave generator) and saw~ (band-limited sawtooth wave generator) are always producing a full-amplitude wave. You control the amplitude of that wave with multiplication, using *~ or some other object that performs a multiplication internally (such as gain~).
This example uses the subpatch from "A useful subpatch for mixing and balancing two sounds", so it requires that you download the file mix~.maxpat and save the file, with that same name, somewhere in the Max file search path.
The function object assists you to make shapes composed of line segments. When you send a bang to the function, it sends out of its second outlet a list of destination value and ramp time pairs suitable for use as input to a line~ object. In that way, the shape shown in the function object serves as a function over time, the shape of which will be enacted by the signal coming out of the line~ object.
The timepoint object automatically and reliably sends out a bang when the specified point in time is reached. How would you specify a point in time, and also make the notification “conditional”, such that it only occurs if a certain condition is met?
Simple linear motion in 2D animation is achieved by interpolating between two points and successively drawing an object at each intermediate point, as demonstrated in the example on Animating 2D graphics.
You can obtain values that change exponentially or logarithmically by using the pow object or by using the pow($f1,$f2) function in the expr object.