Question

The domain of the function f(x) = -2x is restricted to the positive integers. Which values are elements of the range? (Pick all that apply)

A) 0
B) 4
C) -6
D) 6
E) -4
F) -2
G) 2

Answer 1

The elements of the range of the function f(x) = -2x, with the domain restricted to positive integers, are exclusively negative even numbers. The correct options from the given values are -2, -4, and -6.

Step-by-step explanation:

The student has asked which values are elements of the range of the function f(x) = -2x when the domain is restricted to positive integers. To find the range, substitute each positive integer into the function and multiply by -2, following the rules of sign multiplication, and observe the resulting values. Given that negative numbers multiplied with positive numbers result in negative values, the range will consist exclusively of negative even numbers.

• For x=1, f(x) = -2 (1) = -2, therefore F) -2 is in the range.
• For x=2, f(x) = -2 (2) = -4, hence E) -4 is in the range.
• For x=3, f(x) = -2 (3) = -6, which means C) -6 is in the range.

All other positive integers will similarly yield negative even numbers, but the given options do not include them. Therefore, 0, positive values, and negative odd numbers are not in the range when the domain of f(x) is the positive integers.