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What kind of transformation converts the graph of f(x) = -9|x + 1| + 1 into the graph of g(x) = -9|x – 7|?

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What kind of transformation converts the graph of f(x) = -9|x + 1| + 1 into the graph of g(x) = -9|x – 7|?

What kind of transformation converts the graph of f(x) = -9|x + 1| + 1 into the graph of g(x) = -9|x – 7|?
translation 8 units left and 1 unit up
translation 8 units left and 1 unit down
translation 8 units right and 1 unit up
translation 8 units right and 1 unit down




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    1. Quizzma Team

      To determine the transformation from ( f(x) = -9|x + 1| + 1 ) to ( g(x) = -9|x – 7| ), we can analyze the changes in the equation:

      1. The function ( f(x) ) has a vertex at ( (-1, 1) ).
      2. The function ( g(x) ) has a vertex at ( (7, 0) ).

      To find the transformation, we can observe that:

      – The horizontal shift is from ( -1 ) to ( 7 ): this is a shift to the right by ( 8 ) units.

      – The vertical shift from ( 1 ) to ( 0 ) indicates a downward shift by ( 1 ) unit.

      So, the transformation is a translation 8 units right and 1 unit down.

      Therefore, the correct answer is:

      translation 8 units right and 1 unit down.

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