Question

Find the domain and range of f(x) = 72 - 12x.

Option 1: Domain: All real numbers, Range: All real numbers
Option 2: Domain: All real numbers, Range: f(x) ≤ 72
Option 3: Domain: x ≥ 0, Range: f(x) ≤ 72
Option 4: Domain: x ≤ 0, Range: f(x)

Answer 1

The domain and range of the function f(x) = 72 - 12x are both all real numbers, reflecting the function's ability to take any real number value for both x and f(x).

Step-by-step explanation:

To find the domain and range of the function f(x) = 72 - 12x, we need to understand the nature of the function. This function is a linear function with a negative slope, meaning as x increases, f(x) decreases. Since there are no restrictions on the value of x provided in the function itself, the domain is all real numbers. The range of this function is also all real numbers because f(x) can take any value as x varies. However, as x becomes very large, f(x) will decrease without bound, and as x becomes very negative, f(x) will increase without bound.

Considering the options provided:

• • Option 1 would be correct if the statement about the range was modified to reflect that it can decrease without bound.
  • Option 2 states the range incorrectly because the function can take values less than 72.
  • Option 3 and Option 4 impose restrictions on the domain that are not present in the function itself.
• Therefore, the correct domain and range for the function f(x) = 72 - 12x are:
  • Domain: All real numbers
  • Range: All real numbers