Question

Suppose g(x) = f( x +2) - 3. Which statement best compares the graph of g(x) with the graph of f(x)? A. The graph of g(x) is shifted 2 units left and 3 units up. B. The graph of g(x) is shifted 2 units right and 3 units down. C. The graph of g(x) is shifted 2 units left and 3 units down. D. The graph of g(x) is shifted 2 units right and 3 units up.

Answer 1

Given:

The function is:

$g(x)=f(x+2)-3$

To find:

The statement that best compares the graph of g(x) with the graph of f(x).

Solution:

The transformation is defined as

$g(x)=f(x+a)+b$                .... (i)

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.

We have,

$g(x)=f(x+2)-3$               ...(ii)

On comparing (i) and (ii), we get

$a=2$

$b=-3$

Therefore, the graph of g(x) is shifted 2 units left and 3 units down.

Hence, the correct option is C.