The parent function is f(x) = 2^x-6 + 3 and the new function is g(x) = 2^x-3 + 2 How does the graph change fromf (x)tog(x)?
Select each correct answer.
The graph is shifted 3 units right.
The graph is shifted 1 unit up.
The graph is shifted 1 unit down.
The graph is shifted 3 units left.

Options C and D.

Step-by-step explanation:

The given functions are

We need to find the transformation from f(x) to g(x).

Now, write the function g(x) in the form of f(x).

    ...(1)

The translation is defined as

               .... (2)

Where, a is horizontal shift and b is vertical shift.

If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.

If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.

From (1) and (2), we get

, so graph shifts 3 units left.

, so graph shifts 1 unit down.

Therefore, the correct options are C and D.

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