Yes, a horizontal line on a graph is a function.
A function, by definition, requires that each input (x-value) has only one output (y-value). The vertical line test is a common method to determine if a graph represents a function. If any vertical line drawn on the graph intersects it at more than one point, the graph is not a function.
A horizontal line passes the vertical line test because any vertical line will only intersect the horizontal line at a single point. This means for every x-value, there is only one y-value. Therefore, a horizontal line represents a function, specifically a constant function. A constant function has the form f(x) = c, where 'c' is a constant value. The y-value is the same regardless of the x-value.
Example:
Consider the horizontal line y = 3. No matter what x-value you choose (x = -2, x = 0, x = 5, etc.), the corresponding y-value will always be 3.
Key Takeaway:
A horizontal line represents a function where the output (y) is constant for all inputs (x). It satisfies the fundamental requirement of a function: each input has exactly one output.
