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f(x=2x) shrank vertical by factor 1/, shifted 5 units right and 4 up the reflected across the xaxis. Write a equation.

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Answer:

Explanation:

f(x=2x): This stretches the original function f(x) horizontally by a factor of 2. Imagine taking the graph of f(x) and stretching it wider while keeping the same height.



Shrunk vertical by factor 1/: This compresses the vertically stretched function by a factor of 1/2. Imagine squeezing the graph vertically by half.



Shifted 5 units right: This moves the entire graph 5 units to the right. Imagine taking the compressed graph and sliding it 5 units to the right.



Shifted 4 up: This moves the entire graph 4 units up. Imagine taking the right-shifted graph and moving it 4 units up.



Reflected across the x-axis: This flips the entire graph upside down. Imagine taking the up-shifted graph and reflecting it across the horizontal line (x-axis).



Since the original function f(x) is unknown, we can use any placeholder function in the equation. Here, I used f(x-5) to represent the horizontally stretched function after the right shift.



Therefore, the equation f(x) = -1/2 * f(x-5) + 4 represents the final transformed function after all the described changes.



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