Question

Which step is included in the graph of the function f(x)=[x-1]? (the brackets are ceiling functions symbols)

Answer 1

Answer:

A

Step-by-step explanation:

From the definition of a box function y = [x], we know that

y = 0 for, 0 ≤ x < 1

y = - 1 for, - 1 ≤ x < 0

y = - 2 for, - 2 ≤ x < - 1

Here, we are given another box function y = [x - 1], and we have to choose from options the steps which is included in the graph of the this function.

So, the correct step is y = - 5 for, - 4 ≤ x < - 3. (Answer)

Answer 2

we are given

f(x)=[x=1]

where bracket means ceiling functions

we know that

Ceiling  function returns the least value of the integer that is greater than or equal to the specified number

so, we can check each options

option-A:

$-4\leq x$

At x=-4:

f(x)=[-4-1] =-5

For x<-3:

Let's assume

x=-3.1

f(x)=[-3.1-1] =[-4.1]=-5

so, this interval is TRUE

option-B:

$-2\leq x$

At x=-2:

f(x)=[-2-1] =-3

For x<-1:

Let's assume

x=-1.1

f(x)=[-1.1-1] =[-2.1]=-3

so, this is FALSE