Question

Draw the graph of the following function is determine their range.
a. greatest integer function F(x) = (x)
b. f(x) = { 1-x x<0}
{ 1 x=0}
{x+1 x>0}​

Answer 1

Answer:

We've,

[x]=x−{x} for x∈R. Where {x} is the fractional part of x.

Now,

[x]−x=−{x}.

As we've 0≤{x}<1

or, −1<−{x}≤0.

So range of of f(x) is (−1,0].