Final answer:
A graph that is convex but not strictly convex could be a cost function in economics that has a flat region where costs are constant. This flat region denotes a segment of the graph where it is convex due to the line segment between any two points lying on or above the graph, but not strictly convex since it is not above the graph at all points.
Step-by-step explanation:
An example of a graph that is convex but not strictly convex is a graph of a function where part of the graph is a straight line segment. Consider, for example, a piecewise function that has a linear part. If this function has a section that is a horizontal line, the graph is convex because it meets the requirement that a line segment between any two points on the graph lies on or above the graph itself. However, it is not strictly convex because the line segment does not lie strictly above the graph.
A classic example would be the graph of an economic cost function, which often has flat regions where costs are constant, along with regions where the costs increase, forming a convex curve. In these flat regions (the straight line with slope zero), the function is convex but not strictly convex.