What is y=f(2x)?

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The function y = f(2x) represents a horizontal transformation of the original function y = f(x). Specifically, it's a horizontal compression or stretch.

• Horizontal Compression/Stretch: In the case of y = f(2x), the graph of f(x) is horizontally compressed by a factor of 1/2. This means that every x-coordinate on the original graph is halved, effectively squeezing the graph towards the y-axis.

• Transformation of Functions: Understanding how changing the argument of a function (in this case, replacing x with 2x) affects the graph is a key concept in function transformations.

• To find the x-intercepts of y = f(2x), you would set y=0, giving f(2x) = 0. If f(x) = 0 when x = a, then f(2x) = 0 when 2x = a, or x = a/2. The x-intercepts are also compressed by a factor of 1/2.

• The y-intercept remains unchanged. Because the y-intercept occurs when x = 0, we have y = f(2*0) = f(0), which is the same as the y-intercept of y = f(x).