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The graph of F(x), shown below, has the same shape as the graph ofG(x) = x, but it is shifted to the left 3 units. What is its equation?F(x) =A. F(x) = x² - 3B. F(x) = x2 + 3C. F(x) = (x-3)2D. F(x) = (x + 3)?

The graph of Fx shown below has the same shape as the graph ofGx x but it is shifted to the left 3 units What is its equationFx A Fx x 3B Fx x2 3C Fx x32D Fx x class=

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Answer

Option D is correct.

f(x) = (x + 3)²

Explanation

When a function g(x) is translated horizontally along the x-axis by a units, the new function is represented as

f(x + a) when the translation is by a units to the left.

f(x - a) when the translation is by a units to the right.

So, for g(x) = x², translated 3 units to the left,

g(x) becomes g(x + 3) = f(x) = (x + 3)²

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