Question

The value of a machine used in manufacturing is modeled by the function f(x)=16(4/5). where x is the age of the machine in years and f(x) is the value of the machine in thousand dollars. What is the appropriate domain for this function?

1) All real numbers
2) Positive real numbers
3) Non-negative real numbers
4) Non-positive real numbers

Answer 1

The appropriate domain for this function is non-negative real numbers.

Step-by-step explanation:

The appropriate domain for this function is 3) Non-negative real numbers.

Since the age of the machine cannot be negative, the domain must be restricted to non-negative real numbers, meaning x can be any non-negative value. In this case, x represents the age of the machine in years, and it cannot be negative since the machine cannot have negative age.

For example, if the machine is 10 years old, the value of the machine can be calculated by substituting x=10 into the function:

f(10) = 16(4/5) = 12.8 thousand dollars.