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As a real-valued function of a real-valued argument, a constant function has the general form <math>y(x)=c</math> or just <math>y=c</math> .
:'''Example:''' The function <math>y(x)=2</math> or just <math>y=2</math> is the specific constant function where the output value is <math>c=2</math>. The [[___domain of a function|___domain of this function]] is the set of all real numbers ℝ. The [[codomain]] of this function is just {2}. The independent variable ''x'' does not appear on the right side of the function expression and so its value is "vacuously substituted". Namely ''y''(0)=2, ''y''(−2.7)=2, ''y''(π)=2,.... No matter what value of ''x'' is input, the output is "2".
:'''Real-world example:''' A store where every item is sold for the price of 1 euro.
The graph of the constant function <math>y=c</math> is a '''horizontal line''' in the [[plane (geometry)|
In the context of a [[polynomial]] in one variable ''x'', the '''non-zero constant function''' is a polynomial of degree 0 and its general form is <math>f(x) = c \, ,\,\, c \neq 0</math> . This function has no intersection point with the ''x''-axis, that is, it has no [[Zero of a function|root (zero)]]. On the other hand, the polynomial <math>f(x)=0</math> is the '''identically zero function'''. It is the (trivial) constant function and every ''x'' is a root. Its graph is the ''x''-axis in the plane.<ref>{{cite book|title=Advanced Mathematical Concepts - Pre-calculus with Applications, Student Edition|last1=Carter|first1=John A.|last4=Marks|first4=Daniel|last2=Cuevas|first2=Gilbert J.|last3=Holliday|first3=Berchie|last5=McClure|first5=Melissa S. |publisher=Glencoe/McGraw-Hill School Pub Co|year=2005|isbn=978-0078682278|chapter=1|edition=1|page=22}}</ref>
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