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What kind of transformation converts the graph of f(x)=−(x+5)2+10f(x) = -(x + 5)^2 + 10 into the graph of g(x)=−(x+5)2+6g(x) = -(x + 5)^2 + 6?\newlineChoices:\newline(A) translation 44 units left\newline(B) translation 44 units down\newline(C) translation 44 units up\newline(D) translation 44 units right

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Q. What kind of transformation converts the graph of f(x)=−(x+5)2+10f(x) = -(x + 5)^2 + 10 into the graph of g(x)=−(x+5)2+6g(x) = -(x + 5)^2 + 6?\newlineChoices:\newline(A) translation 44 units left\newline(B) translation 44 units down\newline(C) translation 44 units up\newline(D) translation 44 units right
  1. Compare Functions: To determine the type of transformation, we need to compare the two functions f(x)f(x) and g(x)g(x). We will look at the constants at the end of each function to see how they differ.
  2. Identify Difference: The original function is f(x)=−(x+5)2+10f(x) = -(x + 5)^2 + 10. The new function is g(x)=−(x+5)2+6g(x) = -(x + 5)^2 + 6. The only difference between f(x)f(x) and g(x)g(x) is the constant term at the end of the equation.
  3. Calculate Vertical Shift: The constant term in f(x)f(x) is +10+10, and the constant term in g(x)g(x) is +6+6. To go from +10+10 to +6+6, we subtract 44. This means the graph of f(x)f(x) has been moved down by 44 units to get the graph of g(x)g(x).
  4. Determine Transformation: Since the graph has been moved vertically down by 44 units, the correct transformation is a translation 44 units down.

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