What characteristic does a constant function display on a graph?

A constant function is defined as a function that always returns the same value, regardless of the input. This can be expressed mathematically as f(x) = c, where c is a constant. When graphed on a coordinate plane, the y-value remains the same for all values of x, leading to a straight line that is perfectly horizontal.

In this context, a horizontal line indicates that there is no change in the output value as you move along the x-axis; the function does not increase or decrease. This characteristic is visually represented by the horizontal line at the height determined by the constant value. Therefore, the correct answer aligns with the fundamental properties of constant functions, demonstrating that their graphical representation is undeniably horizontal.