Final answer:
To identify the rule defining the graphed function, we investigate the characteristics: quadratic shows a parabolic shape, exponential has a J-curve, logarithmic flattens over time, and linear displays a constant slope as a straight line.
Step-by-step explanation:
To determine which rules define the function graphed, it's important to understand the characteristics of different types of graphs. A quadratic function graph is a parabola that opens upwards or downwards. An exponential function graph consistently increases or decreases at an increasing rate and has a J-curve shape. A logarithmic function graph typically increases or decreases and has a characteristic curve that flattens out as x increases. Lastly, a linear function graph is a straight line with a constant slope. By comparing the graph in the question to these descriptions, we can select the correct rule that defines the function.