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.