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 stretching, compressing, or shifting. In the case of g(x) = (1/2)f(2x), the function undergoes both vertical compression by a factor of 1/2 and horizontal compression by a factor of 1/2, affecting the overall shape and position of the graph.
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Horizontal Scaling
Horizontal scaling involves changing the input values of a function, which affects the width of its graph. In g(x) = (1/2)f(2x), the '2x' indicates that the function f(x) is being evaluated at twice the rate, resulting in a horizontal compression. This means that the graph of g will appear narrower compared to the original graph of f.
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Vertical Scaling
Vertical scaling modifies the output values of a function, impacting the height of its graph. In the expression g(x) = (1/2)f(2x), the factor of 1/2 indicates that the output of f(2x) is halved, leading to a vertical compression. This results in the graph of g being closer to the x-axis than the graph of f, effectively reducing its amplitude.
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