Question

Can some one help plz

Answer 1

Given:

The parent function is

`f(x)=6\left((1)/(8)\right)^x`

The translated function is

`f(x)=6\left((1)/(8)\right)^(x+3)-2`

To find:

The correct statement from the given options.

Solution:

The translation is defined as

`g(x)=f(x+a)+b`

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.

In the parent function we have x in the power but in the translated function we have (x+3). So, a=3>0, the graph shifts 3 units left.

In the translated function, we have b=-2<0, so the graph shifts 2 units down.

The graph of
`f(x)=6\left((1)/(8)\right)^(x+3)-2` is a horizontal shift to the left 3 units and a vertical shift down 2 units from the original function
`f(x)=6\left((1)/(8)\right)^x`.

Therefore, the correct option is A.