Short Answer 
The graph of the function y = 2 csc(x) features x-axis values from -2œA to 2œA and y-axis values from -2 to 6, with vertical asymptotes at x = nœA for integers n. The function has specific intersection points at y = 3 and y = 1, confirming that y = 2 csc(x) accurately represents the given properties.
Step 1: Understand the Key Features of the Graph
The given equation for the graph is y = 2 csc(x). To comprehend this graph, it’s essential to note its distinctive features, including:
- The x-axis ranging from -2œA to 2œA with an interval of œA/2 units.
- The y-axis spanning from -2 to 6 with an interval of 2 units.
- Frequency indicated by its 2œA periodicity.
Step 2: Identify Asymptotes and Intersection Points
Examine the vertical asymptotes of the graph where the function is undefined. For the function y = 2 csc(x), these asymptotes occur at:
- x = nœA for integer values of n.
Additionally, the graph touches specific lines where:
- y = 3 at the points (œA/2, 3) and (-3œA/2, 3).
- y = 1 at the points (3œA/2, 1) and (-œA/2, 1).
Step 3: Analyze Candidate Functions
To choose the correct function fitting these characteristics, we analyze the candidates:
- y = sec(x): This function has asymptotes at x = (2n + 1)œA/2, which do not align with our specified values.
- y = csc(x): This function’s asymptotes are at x = n≈ìA, matching the described positions.
Therefore, to match the outlined properties, the function that accurately fits is y = 2 csc(x).