Final answer:
The correct function that assigns to each nonnegative integer its last digit is f(x) = x mod 10 because the modulus operation gives the remainder of division by 10, which is the last digit of the number. D) f(x) = [x/10]
Step-by-step explanation:
The function that best represents assigning to each nonnegative integer its last digit is f(x) = x mod 10. The reason behind this is that the modulus operation (mod) calculates the remainder of the division of a number by another number. In this case, dividing any nonnegative integer by 10 and then finding the remainder will always give us the last digit of that integer because the base-10 number system is decimal, meaning every increase by a power of ten represents a new place value.
For example, if we take the number 123 and apply the function f(x) = x mod 10, we get:
f(123) = 123 mod 10 = 3
This is because 123 divided by 10 is 12 with a remainder of 3, which is the last digit of 123. The options A, C, and D do not yield the last digit of a nonnegative integer. Squaring a number does not isolate the last digit (Option A), taking the root could potentially return a number with different last digit especially in non-perfect squares (Option C), and dividing a number by 10 without the modulus (Option D) effectively removes the last digit instead of isolating it.