Question

State the domain and range of the function M(x) = 2⌊x⌋.

a. Reals, all integers
b. Reals, positive integers
c. Even integers
d. All integers

Answer 1

The domain of the function M(x) = 2⌊x⌋ is all real numbers. The range of the function M(x) = 2⌊x⌋ is all even integers.

Step-by-step explanation:

The domain of the function M(x) = 2⌊x⌋ is all real numbers. This is because the function does not have any restrictions on the value of x.

The range of the function M(x) = 2⌊x⌋ can be found by considering the range of the floor function, which is all integers. So, the range of M(x) is all even integers, since multiplying an integer by 2 gives an even integer.

Therefore, the correct answer is c. Even integers.