In the context of graphing functions, which term describes the rate of change?

The term that describes the rate of change in the context of graphing functions is steepness. This concept is closely related to the slope of a line or curve when graphing a function. The steeper the graph, the greater the rate of change; this means that for a given increase in the x-value, there is a larger increase (or decrease) in the y-value.

In linear functions, the slope reflects the steepness directly and indicates how much y changes for a unit change in x. A positive slope means the function is increasing, while a negative slope indicates a decrease. For non-linear functions, the notion of "steepness" can vary at different points, but the underlying principle remains that steepness is a measure of how quickly y changes in relation to x.

Other terms like constant, direction, and symmetry may relate to the behavior and characteristics of graphs, but they do not specifically address the notion of the rate at which one variable changes compared to another. Constant refers to situations where there is no change, direction pertains to whether a function is increasing or decreasing, and symmetry addresses how a graph may mirror itself over a particular axis, none of which uniquely signifies rate of change as steepness does.