Question

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

Answer 1

A

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

A step that is included in the graph of the function f(x)=[x-1] is: A. -4 ≤ x < -3 → y = -5.

In Mathematics and Euclidean Geometry, a ceiling function is sometimes referred to as the least integer function of a real number (x) and it can be defined as the smallest integer that is not smaller than x. Additionally, a ceiling function is denoted by this mathematical symbol [x].

Based on the definition of a ceiling function f(x) = [x], we have the following steps;

f(x) = 0, for 0 ≤ x < 1

f(x) = -1, for -1 ≤ x < 0

f(x) = -2, for -2 ≤ x < -1

f(x) = -3, for -3 ≤ x < -2

f(x) = -4, for -4 ≤ x < -3

f(x) = -5, for -5 ≤ x < -4

Since the graph of the parent ceiling function f(x) = [x] was horizontally shifted to the right to produce the graph of f(x) = [x - 1], a step that would be included in the graph of this ceiling function is given by;

-4 ≤ x < -3 → y = -5.

f(x) = -5, for, -4 ≤ x < -3.