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Incnis Mrsi (talk | contribs) Undid revision 590727442 by Staszek Lem (talk) removed an EXPLICIT statement about the degree of a polynomial. also, we have not an article specifically about the graph, so it is topical |
Lembit Staan (talk | contribs) →Relationship with other classes of functions: well, if it is topical, then don't make topical confusion |
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== Relationship with other classes of functions ==
If the coefficient of the variable is not zero ({{math|''a'' ≠ 0}}), then a linear function 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
A straight line, when drawn in a different kind of coordinate system may represent other functions.
The graph of a linear function also represents an [[exponential 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 the graph of a linear function represents a [[power law]]:▼
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If ''both'' [[___domain of a function|arguments]] and values of a function are in the logarithmic scale (i.e., when {{math|[[logarithm|log]](''y'')}} is a linear function of {{math|[[logarithm|log]](''x'')}}), then the straight line represents a [[power law]]:
:<math>\log_r y = a \log_r x + b \quad\Rightarrow\quad y = r^b\cdot x^a</math>
On the other hand, the graph of a linear function in terms of [[polar coordinates]]:
:<math>r =f(\varphi ) = a\varphi + b</math>
is an [[Archimedean spiral]] if <math>a \neq 0</math> and a [[circle]] otherwise.
== Notes ==
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