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 defined for x ≥ 0 and produces non-negative outputs. Its graph is a curve that starts at the origin (0,0) and increases gradually, reflecting the relationship between x and its square root. Understanding this function is crucial as it serves as the foundation for applying transformations in the given problem.
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Imaginary Roots with the Square Root Property
Graph Transformations
Graph transformations involve shifting, stretching, compressing, or reflecting the graph of a function. In this case, the function h(x) = √(x+1) - 1 represents a horizontal shift to the left by 1 unit and a vertical shift downward by 1 unit. Mastery of these transformations allows for the accurate graphing of new functions based on known ones.
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Function Composition
Function composition refers to the process of applying one function to the results of another. In the context of h(x), the inner function (x + 1) modifies the input of the square root function, while the outer function (subtracting 1) adjusts the output. Understanding how to compose functions is essential for manipulating and graphing complex functions derived from simpler ones.
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