Final answer:
To determine whether a mathematical function undergoes vertical expansion or compression, compare the absolute value of the coefficient of the function's output to 1; values greater than 1 indicate an expansion, while values between 0 and 1 indicate a compression.
Step-by-step explanation:
To tell between vertical expansion or compression in mathematics, particularly in graph transformations, you can look at the coefficient of the function's output. If a function f(x) is multiplied by a factor a where |a| > 1, the graph of y = a f(x) represents a vertical expansion because the values of y are stretched away from the x-axis. Conversely, if 0 < |a| < 1, the graph of y = a f(x) shows a vertical compression, as the values of y are squeezed closer to the x-axis.
As an example, if we take the base function f(x) = x2 and the transformed function g(x) = 2x2, the graph of g(x) would show a vertical expansion because the coefficient 2 stretches the parabolic graph vertically. However, if we consider h(x) = 0.5x2, the graph of h(x) would present a vertical compression because the coefficient 0.5 compresses the graph towards the x-axis.