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