what is the constant function
Answers
Step-by-step explanation:
As a real-valued function of a real-valued argument, a constant function has the general form {\displaystyle y(x)=c} y(x)=c or just {\displaystyle y=c} y=c .
Example: The function {\displaystyle y(x)=2} y(x)=2 or just {\displaystyle y=2} y=2 is the specific constant function where the output value is {\displaystyle c=2} c=2. The 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 {\displaystyle y=c} y=c is a horizontal line in the plane that passes through the point {\displaystyle (0,c)} (0,c).[4]
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 {\displaystyle f(x)=c\,,\,\,c\neq 0} f(x)=c\,,\,\,c\neq 0 . This function has no intersection point with the x-axis, that is, it has no root (zero). On the other hand, the polynomial {\displaystyle f(x)=0}