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a linear equation is simply an equation in the form x+y quadratics, cubics and quartics are all non-linear, and are in the following forms Quadratics - x^2+x+y Cubics - x^3+x^2+x+y Quartics - x^4+x^3+x^2+x+y
They are not. A vertical line is not a function so all linear equations are not functions. And all functions are not linear equations.
Linear equations are a small minority of functions.
Most functions are not like linear equations.
It can be anything that you choose it to be. It can be the whole real line or any proper subset - including disjoint subsets. It can be matrices, all of the same dimensions (Linear Algebra is based on them) or a whole host of other alternatives.