In a three-variable graph, which axis would typically display the dependent variable when using three axes (x, y, z)?

• A. X-axis
• B. Y-axis
• C. Z-axis
• D. Time axis

Answer: (C)

When a function depends on two inputs, the way we visualize its output is by using the two inputs on the horizontal axes (x and y) and plotting the resulting value as height above the plane along the third axis. The dependent variable is represented by the Z axis because it encodes the output of the function for each pair of inputs (x, y). This setup lets you see how z changes as x and y vary, forming a surface in three-dimensional space. The time axis isn’t the standard choice here unless you’re explicitly modeling something that evolves over time; in a typical three-variable graph, the dependent variable sits on the Z axis.