If a linear function is defined for all real numbers, what is its domain?

If a linear function is defined for all real numbers, what is its domain?

• A. All real numbers.
• B. Only nonnegative numbers.
• C. All positive numbers.
• D. A finite interval.

Answer: (A)

Domain refers to the set of input values x for which the function is defined. For a linear function with real coefficients, there are no restrictions on x, so you can substitute any real number and get a real output. That means the domain is all real numbers. Visually, a straight line stretches without end in both directions, reflecting inputs from every real number. The other options would require limiting the inputs (to nonnegative, positive, or a finite interval), which isn’t the case here.

Domain refers to the set of input values x for which the function is defined. For a linear function with real coefficients, there are no restrictions on x, so you can substitute any real number and get a real output. That means the domain is all real numbers. Visually, a straight line stretches without end in both directions, reflecting inputs from every real number. The other options would require limiting the inputs (to nonnegative, positive, or a finite interval), which isn’t the case here.