Question

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4. The function f(x) goes through the point (2, 6). What point will this translate to in the function f(x) = (x + 2) - 3?
(0,9)
(0,3)
(4,9)
(4,3)
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Answer 1

The function f(x) = (x + 2) - 3 is a horizontal translation two units to the left and a vertical translation three units down of the original function f(x). Therefore, the point (2, 6) on the graph of the original function is translated to the point (0, 3) on the graph of f(x) = (x + 2) - 3.

The point that (2, 6) translates to in the function f(x) = (x + 2) - 3 is 2) (0,3).

The function f(x) = (x + 2) - 3 shifts the graph of the original function f(x) two units to the left and three units down. This means that any point on the graph of the original function will be shifted two units to the left and three units down to get its corresponding point on the graph of f(x) = (x + 2) - 3.

Therefore, the point (2, 6) on the graph of the original function will be shifted to the point (2 - 2, 6 - 3) = (0, 3) on the graph of f(x) = (x + 2) - 3.

So the answer is (0, 3).

The image of the graph is attached with the answer.