Do ordinary linear functions have any such property?
They do. Any linear function at all has the same property when b is 1 – a. Thus for any linear function at all we have f(ax + (1 – a)z) = a f(x) + (1 – a) f(z) But be careful, linear functions that are not homogeneous do not obey the general linearity property stated several lines above. Properties like these mean that once you know the value of a linear function at two arguments you can easily find its value anywhere else it is defined. The property here described is often called the property of linearity. This is not really a sensible way to describe it because perfectly good linear functions which have y intercept that is not 0 do not obey the more general version of the property (the first one above.) Anyway, realize that most functions DO NOT have either of these properties. 3A Describing Linear Functions on a Spreadsheet Suppose we have a linear function, say, f(x) = 5x + 3. We now address the following questions: 1. How can we evaluate this function at an arbitrary argument, x,
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