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Write an equation for each type of transformation that can be used to transform f(x) to g(x)?

User Arjit
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Final answer:

To transform f(x) to g(x), apply equations for translations, stretching/compressing, and reflections, substituting known values and checking for logical consistency.

Step-by-step explanation:

To transform a function f(x) to another function g(x), we can apply a variety of transformations which include translations, stretching or compressing, and reflections. Here are the possible equations representing these transformations:

• Translation: To shift the graph of f(x) horizontally or vertically, you would use g(x) = f(x - h) + k, where h represents the horizontal shift and k the vertical shift.

• Stretching or Compressing: To stretch the graph vertically by a factor of a, use g(x) = a·f(x). If a is less than 1, this would compress the graph. For horizontal stretching by a factor of b, use g(x) = f(x/b).

• Reflection: Reflect f(x) across the x-axis with g(x) = -f(x), or across the y-axis with g(x) = f(-x).

When performing these transformations, make sure to substitute known values with proper units, and check if the transformed equation for g(x) makes sense in the context of the problem.

User Rachel Quick
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