f: R R

f(x) = |x| for each x ∈ R

 

Here |x| is known as modulus of x

|x| is always positive.

So, |–1| = 1

|–2| = 2

|1| = 1

|2| = 1

|0| = 0

 

Let us rewrite the function

Modulus function for x greater than and less than 0.jpg


Let’s check for different values of x

For x = –1

x < 0

So, f(x) = – x

f(x) = – (–1) = 1

 

For x = –2

x < 0

So, f(x) = – x

f(x) = – (–2) = 2

 

For x = 1

x > 0

So, f(x) = x

f(x) = 1

 

For x = 2

x > 0

So, f(x) = x

f(x) = 2

 

For x = 0

x ≥ 0

So, f(x) = x

f(x) = 0

 


Now,

Plotting graph

Modulus Function.jpg

Here,

Domain = All values of x = R

 

Range = All values of y

Since y will always be positive or 0

Range = All positive Real numbers and 0

  1. Chapter 2 Class 11 Relations and Functions
  2. Concept wise
Ask Download

About the Author

Davneet Singh's photo - Teacher, Computer Engineer, Marketer
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.