Question

Shift f(x)=x^2 three units to the left and four units down

Answer 1

Given:

The parent sine function is $f(x)=x^2$.

It shifts three units to the left and four units down.

To find:

The new function.

Solution:

The translation is defined as

$f_1(x)=f(x+a)+b$                .... (1)

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.

Graph shifts 3 units to the left. So, a=3.

Graph shifts 4 units down. So, b=-4.

Putting a=3 and b=-4, we get

$f_1(x)=f(x+3)-4$

$f_1(x)=(x+3)^2-4$          $[\because f(x)=x^2]$

Here, new function is also defined by f(x). So, $f(x)=(x+3)^2-4$.

Therefore, the correct option is d.