Here are the essential concepts you must grasp in order to answer the question correctly.
Function Transformation
Function transformation refers to the process of altering the graph of a function through various operations, such as shifting, stretching, or reflecting. In this case, adding a constant to the function, like g(x) = f(x) + 2, results in a vertical shift of the graph of f(x) upwards by 2 units.
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Vertical Shift
A vertical shift occurs when a function is adjusted by adding or subtracting a constant from its output. For example, in g(x) = f(x) + 2, every point on the graph of f(x) is moved up by 2 units, which affects the y-coordinates of all points on the graph while leaving the x-coordinates unchanged.
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Graph Interpretation
Graph interpretation involves analyzing the features of a graph, such as its shape, intercepts, and asymptotes, to understand the behavior of the function it represents. When graphing g(x) based on f(x), one must recognize how the vertical shift alters these features, ensuring an accurate representation of the new function.
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