Question

Which of the following represents the function that assigns to each nonnegative integer its last digit?

A) f(x) =x
B) (f(x) = x \mod 10\)
C) f(x) = [x/10]
D) f(x) = 10-x

Answer 1

The function that assigns to each nonnegative integer its last digit is f(x) = x mod 10. Option B is the correct representation of this function as it provides the remainder of x divided by 10, hence, the last digit.

Step-by-step explanation:

The function that assigns to each nonnegative integer its last digit is best represented as f(x) = x mod 10. Let's break down the options to see why this is the correct choice:

• f(x) = x simply assigns to each nonnegative integer itself, which does not satisfy the requirement of the function in question.
• f(x) = x mod 10 takes any nonnegative integer x and returns the remainder when x is divided by 10, which effectively gives us the last digit of x. This is the correct representation of the function.
• f(x) = [x/10] takes the integer part of the result when x is divided by 10, which does not give us the last digit but rather removes the last digit from x.
• f(x) = 10-x subtracts x from 10, which does not relate to the last digit of x in any consistent way.

Therefore, the correct answer is option B, which is f(x) = x mod 10.