Linear function (calculus): Difference between revisions

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== Relationship with other classes of functions ==

Linear functions are a particular kind of polynomial functions. If the coefficient on the variable is not zero ({{math|''a'' ≠ 0}}), then it is represented by a [[degree of a polynomial|degree]] 1 polynomial (also called a ''linear polynomial''), otherwise it is a [[constant function]] – also a polynomial function, but of lower degree.

Linear functions are a particular kind of [[polynomial function]].

A linear function also representrepresents an [[Exponentialexponential growth|exponential function]] whose [[codomain|values]] are expressed in the [[logarithmic scale]]. It means that when {{math|[[logarithm|log]](''g''(''x''))}} is a linear function of {{mvar|x}}, the function {{mvar|g}} is exponential. With linear functions, increasing the input by one unit causes the output to increase by a fixed amount, which is the slope of the graph of the function. With exponential functions, increasing the input by one unit causes the output to increase by a fixed multiple, which is known as the base of the exponential function. If ''both'' [[___domain of a function|arguments]] and values of a function are in the logarithmic scale, then a linear function represents a [[power law]]:

:<math>\log_r y = a \log_r x + b \quad\Rightarrow\quad y = r^b\cdot x^a</math>

== Notes ==