Given information:
Consider the function.
For all real numbers
h(x)=⌈x⌉−⌊x⌋
The objective is to graph this function.
Concept used:
Calculation:
The objective is to graph this function.
Let x be a real number.
A floor function of x is denoted by f(x)=⌊x⌋ and is defined by the greatest integer that is less than or equal to x.
A ceiling function of x is denoted by f(x)=⌈x⌉ and is defined by the smallest integer that is greater than or equal to x.
The function h(x)=⌈x⌉−⌊x⌋ is the difference of ceiling function and floor function.
Now, examine the function h(x) for the small interval x∈(0,1).
⌈0.5⌉=1 and ⌊0.5⌋=0h(0.5)=⌈0.5⌉−⌊0.5⌋=1−0=1
Now, examine the function h(x) for the small interval x∈(−1,0).
⌈−0.5⌉=1 and ⌊−0.5⌋=−1h(−0.5)=⌈−0.5⌉−⌊−0.5⌋=0−(−1)=1
Next, examine the function h(x) for integer value.
x=−1
⌈−1⌉=−1 and ⌊−1⌋=−1h(−1)=⌈−1⌉−⌊−1⌋=−1−(−1)=0
Next, examine the function h(x) for integer value.
x=1⌈1⌉=1 and ⌊1⌋=1h(1)=⌈1⌉−⌊1⌋=1−(1)=0
Define a step function h(x) as below