Question

What is Modulus Function??
Give it's Range & Domain?​

Answer 1

Answer:

The graph of the modulus function, f(x) = |x| is attached below :

Modulus Function : A modulus function is a function which gives only positive output irrespective of the input.

Domain : The modulus function can take any value of x . So, its domain constitutes of all the real numbers.

⇒ Domain : (-∞ , ∞)

Range : For every real number whether positive or negative, it gives same positive real number but with a positive sign. So, its range is all positive real numbers.

⇒ Range : [ 0 , ∞ )

Answer 2

Answer:

Modulus Function is defined as the real valued function f:R→Rf:R→R , y = |x| for each x∈Rx∈R 

For each non-negative value of x, f(x) is equal to x. But for negative values of x, the value of f(x) is the negative of the value of x

f(x)=|x|={x if x≥0−x if x<0f(x)=|x|={x if x≥0−x if x<0

It is also called the absolute value function

Example

|-3| =3

|-2|=2

|2|=2

We know that all the real number can be plotted on the real number line. The absolute value function is used to measure the distance between two numbers on the number line.. Thus, the distance between x and 0 is |x - 0| = |x|. So |x| represent the distance of the number from the origin.Similarly the distance between x and y is |x - y|. Thus, the distance from -3 to -1 is |-3 - (-1)| = |-3 + 1| = |2| = 2, and the distance from -3 to 5 is |-3 - 5| = |-8| = 8

Domain and Range of the Modulus Function(absolute value function) 

For f:R→R,y=f(x)=|x|f:R→R,y=f(x)=|x| for each x∈Rx∈R

Domain = R 

Range = R+=x∈R:x≥0R+=x∈R:x≥0

Graph of the Modulus Function

The graph of the modulus function is shown below. It coincide with the graph of identity function y=x for x≥0x≥0 and for x< 0, it is a graph of linear function y=-x