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Choose the function that correctly identifies the transformation of f(x) = x 2 shifted two units down and one unit to the left. g(x) = (x - 1)2 - 2 g(x) = (x - 1)2 + 2 g(x) = (x + 1)2 - 2 g(x) = (x + 1)2 + 2

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Answer:

[tex]g(x) = ( { x + 1})^{2} - 2[/tex]

Step-by-step explanation:

The parent function is

[tex]f(x) = {x}^{2} [/tex]

A transformation that involves a downward shift h units and a shift to the left k units is of the form:

[tex]f(x + k) - h[/tex]

If the function is shifted two units down and and one unit to the left, then

[tex]g(x) = ( { x + 1})^{2} - 2[/tex]

Therefore the third choice is correct.

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