Question

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.

Answer 1

Options C and D.

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<0`, so graph shifts 1 unit down.

Therefore, the correct options are C and D.