Modulus Function

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

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

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