Check sibling questions

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 - Part 2

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

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.