ZERO FUNCTION : The zero function is a function whose domain consists of all real numbers, and its range consists of a single element, which is 0. It is also considered a constant function because its value remains unchanged regardless of the input changes. In this article, we will delve into the properties and nature of the zero function.
A zero function is a constant function where the output value is consistently zero, regardless of the input values. The input of a zero function can be any real number, while the output is always fixed at 0. Because every element in the domain maps to 0, the zero function is not a one-to-one function.
ZERO FUNCTION MEANING : A function F : R -> defined as f(x)=0 for all values of x in the real numbers is called a zero function. The range of a zero function is a singleton set, specifically {0}. Just like any other constant function graph parallel to the x-axis, the graph of the zero function coincides with the x-axis itself since the y-coordinate is always 0 throughout the graph. It is a many-to-one function because all elements in the domain have the same image, which is 0.
ZERO FUNTION GRAPH : The graph of a zero function f(x) = 0 is similar to other constant functions graphs which are parallel to the x-axis. Any function can be considered as a constant function if it is of the form y = k, where k is a constant and k is any real number. It is also written as f(x) = k. Since the range is zero for the zero function and the value of the y-coordinate is always zero, therefore the graph of the zero function is the X-axis itself. In other words, we can say that the zero function graph is the horizontal axis.