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Can some one help plz

Can some one help plz-example-1
User Gdupras
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1 Answer

6 votes

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.

User Nikita Leonov
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5.1k points