Question

Below the graph of Translate it to become the graph of

Answer 1

Given:

`y=((1)/(4))^x`

Required:

Translate it to the graph of

`y=((1)/(4))^(x-1)-2`

Step-by-step explanation:

Rewrite the function as:

`\begin{gathered} y=((1)/(4))^x((1)/(4))^(-1)-2 \\ y=4((1)/(4))^x-2 \end{gathered}`

To graph the function

`y=4((1)/(4))^x`

multiply all the y- coordinates of the function

`y=((1)/(4))^x`

by 4. Since 4>1, so the graph has a vertical stretching.

The graph of

`y=4((1)/(4))^x-2`

shift the graph of

`y=4((1)/(4))^x`

2 units down by subtracting 2 from the y-coordinate of the points of the graph

`y=4((1)/(4))^(x)`

Thus the graph of

`y=((1)/(4))^(x-1)-2`

Final Answer: