How can you visually determine if a function is increasing on a graph?

A function is considered increasing on an interval when, as you move from left to right along the graph, the y-values of the function increase. This means that for any two points on the function within the interval, if you select a point to the left (with a smaller x-value), the corresponding y-value will be less than the y-value of the point to the right (with a larger x-value).

In a graph, this visual representation manifests as a line that moves upwards as you progress from left to right. Thus, when the graph rises to the right, it indicates that the function is increasing in that region. This rising behavior shows that as x increases, y increases, fulfilling the criteria for an increasing function.

When examining other options, falling to the right indicates a decreasing function, rising to the left does not fit the definition of an increasing function, and a function being linear does not provide information regarding the increasing or decreasing nature unless the slope is specified. Therefore, the indication of a graph that rises to the right is a clear and accurate way to determine that a function is increasing.