Short Answer 
To determine the function represented by a graph, first eliminate functions based on key properties, such as the graph not passing through the origin. Next, pinpoint specific coordinates that depict the graph’s characteristics, and finally, calculate the function’s period and frequency to further establish its mathematical behavior.
Step 1: Analyze the Graph and Eliminate Options
Begin by reviewing the properties of the graph to determine which function can be eliminated. Since the graph does not pass through the origin, any function that includes sine can be discarded. Additionally, check the value at x = 0; if it results in a positive outcome, that function can also be eliminated. This process will help narrow down your choices significantly.
Step 2: Identify Specific Points on the Graph
Next, locate specific points on the graph to provide clear identification of the function. For example, note that Point A is approximately at (1.57, 0), which corresponds to (≈ìA/2, 0), and Point B is at (3.14, -2), equivalent to (≈ìA, -2). These coordinates will guide your understanding of the graph’s behavior and characteristics.
Step 3: Determine Period and Frequency of the Function
Finally, analyze the function to calculate its period and frequency. For instance, if the function has a period of œA, you can derive the frequency using the formula: Frequency = 1/Period. Thus, for a period of œA, the frequency would be 1/œA. This foundational knowledge is crucial for establishing the mathematical characteristics of the desired function.