Determine whether the given table of values must be from a nonlinear function or could be from a linear function.
First, let’s define what we mean by a linear function. A linear function is an equation whose graph is a straight line. And that means the best way to check if this is a linear or nonlinear function is to graph these four points. We know that when 𝑥 equals zero, 𝑦 equals three. We also know that when 𝑥 equals two, 𝑦 equals four. When 𝑥 equals four, 𝑦 equals five. And when 𝑥 equals six, 𝑦 equals six. Looking at this graph, it does seem like these points would connect to form a straight line. And that means it could be from a linear function. Our other option said that it must be from a nonlinear function.
There’s nothing in these four points that would make this a nonlinear function. We know that nonlinear functions are functions which are not linear. If we think of some examples, a quadratic function is nonlinear. Other type of polynomial functions are also nonlinear. But again, the example we’re given does appear to be in a straight line. There is a constant rate of moving to the right two and up one, to the right two and up one. And, again, to the right two and up one. And so, the best answer we can give is that it could be a linear function. There’s no reason to say that these four points must form a nonlinear function.