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What kind of transformation converts the graph of f(x)=7∣x−4∣+5f(x)=7|x-4|+5 into the graph of g(x)=7∣x−2∣+3g(x)=7|x-2|+3?

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Q. What kind of transformation converts the graph of f(x)=7∣x−4∣+5f(x)=7|x-4|+5 into the graph of g(x)=7∣x−2∣+3g(x)=7|x-2|+3?
  1. Identify Changes: Identify the changes in the absolute value expression and the constant term. f(x)=7∣x−4∣+5f(x) = 7|x - 4| + 5 changes to g(x)=7∣x−2∣+3g(x) = 7|x - 2| + 3. The absolute value expression changes from ∣x−4∣|x - 4| to ∣x−2∣|x - 2|, indicating a horizontal shift. The constant term changes from +5+5 to +3+3, indicating a vertical shift.
  2. Determine Shift: Determine the horizontal shift.\newlineThe shift from ∣x−4∣|x - 4| to ∣x−2∣|x - 2| suggests a shift to the right by 22 units.\newlineTo confirm, consider a test point. If x=4x = 4 in f(x)f(x), then x=4−2=2x = 4 - 2 = 2 should be used in g(x)g(x) for the same yy-value.\newlineCheck: f(4)=7∣4−4∣+5=5f(4) = 7|4 - 4| + 5 = 5 and g(2)=7∣2−2∣+3=3g(2) = 7|2 - 2| + 3 = 3.

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