Question

The parent function is f(x) = 2^x-6 + 3 and the new function is g(x) = 2^x-3 + 2

Answer 1

Answer:

Options C and D.

Step-by-step explanation:

The given functions are

$f(x)=2^{x-6}+3$

$g(x)=2^{x-3}+2$

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

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

$g(x)=2^{x+3-3-3}+2+1-1$

$g(x)=[2^{(x+3)-6}+3]-1$

$g(x)=f(x+3)-1$     ...(1)

The translation is defined as

$g(x)=f(x+a)+b$                .... (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

$a=3>0$, so graph shifts 3 units left.

$b=-1$, so graph shifts 1 unit down.

Therefore, the correct options are C and D.