2
AssignmentMultiple Select

Step Functions

Question 2 • VA-Mathematical Analysis

Does your answer include the following?

Answer
A
The statement is not true for all real numbers. It is only true for decimal or fractional values of x .
B
If x is an integer, then the ceiling function returns x when the input is x . But, the flooring function returns x + 1 when the input is x + 1.
C
Since x does not equal x + 1 when x is an integer, the expressions are not equal when x is an integer.

Explanation

For the expressions ceil(x) and floor(x + 1), the equality holds when x is not an integer: both values are the next integer above x. If x is an integer, ceil(x) = x, while floor(x + 1) = x + 1, so the values differ. Thus the equality is not true for all real numbers, and all three statements describe this correctly.

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