Here are the essential concepts you must grasp in order to answer the question correctly.
Cotangent Function
The cotangent function, denoted as cot(x), is the reciprocal of the tangent function. It is defined as cot(x) = cos(x)/sin(x). The graph of the cotangent function has vertical asymptotes where sin(x) = 0, which occurs at integer multiples of π. Understanding the basic shape and periodicity of the cotangent function is essential for analyzing its transformations.
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Transformations of Functions
Transformations of functions involve shifting, reflecting, stretching, or compressing the graph of a function. For the cotangent function, horizontal shifts can be represented by adding or subtracting a constant inside the function's argument, such as cot(x + π/2). Recognizing how these transformations affect the graph is crucial for identifying the correct equation from a given graph.
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Vertical Asymptotes
Vertical asymptotes are lines that a graph approaches but never touches or crosses. For the cotangent function, vertical asymptotes occur at x = nπ, where n is an integer. In the provided graph, the locations of these asymptotes help determine the function's behavior and are key indicators for selecting the correct cotangent equation based on the graph's features.
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