Shift f(x)=x^2 three units to the left and four units down a) f(x)=(x+4)^2 -3
b) f(x)=(x-4)^2 -3
c) f(x)=(x-3)^2 -4
d) f(x)=(x+3)^2 -4

Given:

The parent sine function is .

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

To find:

The new function.

Solution:

The translation is defined as

               .... (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

Here, new function is also defined by f(x). So, .

Therefore, the correct option is d.

32

step-by-step explanation:

answer: x=3 and y=4

step-by-step explanation: