Which type of function has a graph that is a horizontal line?

Which type of function has a graph that is a horizontal line?

• A. Linear
• B. Quadratic
• C. Cubic
• D. Constant

Answer: (D)

A constant function outputs the same y-value for every input. Its graph is a horizontal line y = c, where c is that constant. This shows zero change in y as x varies. Linear functions are straight lines with a slope; they would be horizontal only if that slope were zero, which would make them the same as a constant function, but in this context the horizontal graph identifies a constant function. Quadratic and cubic functions produce curves that bend up or down (parabolas or cubic waves), not a flat horizontal line.

A constant function outputs the same y-value for every input. Its graph is a horizontal line y = c, where c is that constant. This shows zero change in y as x varies. Linear functions are straight lines with a slope; they would be horizontal only if that slope were zero, which would make them the same as a constant function, but in this context the horizontal graph identifies a constant function. Quadratic and cubic functions produce curves that bend up or down (parabolas or cubic waves), not a flat horizontal line.