A function is a relationship between a set of inputs and a set of outputs. The key
requirement is that each allowable input relates to exactly one output value.
Equations are often used to define a function. That is, the relationship is given by a rule that tells how to find the output from any given input.
For example f(x)= 7x-2 says in words, given an input number, say x, multiply it by 7 and subtract 2, to get the associated output.
7x - 2 is called a linear expression because its highest power is one (and a function defined by a linear expression is called a linear function. )
A linear equation is an equation between two linear expressions.
Example: 2x + 3 = 7x - 2.
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There is one form of linear equation that is not a function, and that is when x = c, where c is a constant.
A linear function is a function, or equation, that when graphed, will form a straight line.
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A linear function is a function whose graph is a straight line.
A polynomial equation of order >1 that is, where the power of the variable is greater than 1 is a non linear function. A transcendental function is one that cannot be expressed as a finite number of algebaraic operations (addition, multiplication, roots). The exponential and trigonometric functions (and their inverses) are examples.