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.
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Imaginary Roots with the Square Root Property
Graph Transformations
Graph transformations involve shifting, reflecting, stretching, or compressing the graph of a function. For the function h(x) = √(-x + 1), the negative sign indicates a reflection across the y-axis, and the '+1' indicates a horizontal shift to the right. Mastery of these transformations allows for the accurate graphing of modified functions based on the original square root function.
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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) = √(-x + 1), we can view it as a composition of the square root function with a linear transformation. Understanding how to compose functions is essential for manipulating and graphing complex functions derived from simpler ones.
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