A constant function is best described as.

A constant function is best described as.

• A. f(x) = c where c is a constant.
• B. f(x) = x.
• C. f(x) = mx + b.
• D. f(x) = x^2.

Answer: (A)

A constant function is one whose value does not depend on the input. No matter what x you plug in, the output stays the same. This is exactly described by f(x) = c, where c is a fixed constant. Graphically, it’s a horizontal line at height c, with slope zero and a single output value for every input. Other forms change as x changes: f(x) = x yields different values for different x, so it’s not constant; f(x) = mx + b represents a line whose value varies with x unless the slope m is zero (but as written it’s not necessarily constant); f(x) = x^2 also changes with x, giving different outputs.

A constant function is one whose value does not depend on the input. No matter what x you plug in, the output stays the same. This is exactly described by f(x) = c, where c is a fixed constant. Graphically, it’s a horizontal line at height c, with slope zero and a single output value for every input.

Other forms change as x changes: f(x) = x yields different values for different x, so it’s not constant; f(x) = mx + b represents a line whose value varies with x unless the slope m is zero (but as written it’s not necessarily constant); f(x) = x^2 also changes with x, giving different outputs.