Here are the essential concepts you must grasp in order to answer the question correctly.
Square Root Function
The square root function, f(x) = √x, is a fundamental mathematical function that returns the non-negative square root of x. Its graph is a curve that starts at the origin (0,0) and increases gradually, only existing in the first quadrant of the Cartesian plane. Understanding this function is crucial as it serves as the base for further transformations.
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Transformations of Functions
Transformations of functions involve shifting, stretching, compressing, or reflecting the graph of a function. For example, adding a constant inside the function's argument shifts the graph horizontally, while multiplying the function by a constant scales it vertically. In the case of g(x) = 2√(x+1), the graph of f(x) is shifted left by 1 unit and stretched vertically by a factor of 2.
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Graphing Techniques
Graphing techniques involve plotting points and understanding the behavior of functions to create accurate representations of their graphs. This includes identifying key features such as intercepts, asymptotes, and the overall shape of the graph. For the function g(x), applying transformations to the base graph of f(x) allows for a clear visualization of how the function behaves in relation to its parent function.
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