Which of the following statements describes the transformation indicated by:
f(x) = x^2 becomes g(x) = (x - 3)^2
(1 point)
Responses
Function f was translated (shifted) horizontally 3 units to the left.
Function f was translated (shifted) horizontally 3 units to the left.
Function f was translated (shifted) vertically 3 units down.
Function f was translated (shifted) vertically 3 units down.
Function f was translated (shifted) horizontally 3 units to the right.
Function f was translated (shifted) horizontally 3 units to the right.
Function f was translated (shifted) vertically 3 up. -6
Function f was translated (shifted) vertically 3 up. -6
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1 answer
The transformation from \( f(x) = x^2 \) to \( g(x) = (x - 3)^2 \) involves a horizontal shift. The general form of a quadratic function \( f(x) = (x - h)^2 \) indicates a horizontal shift by \( h \) units.
In this case, since \( g(x) = (x - 3)^2 \), the function \( f(x) \) is shifted 3 units to the right.
Therefore, the correct statement is:
Function f was translated (shifted) horizontally 3 units to the right.
