Transforming a function involves changing the position of a function.
The function on the graph is: [tex]\mathbf{g(x) = (\frac{1}{4})^x - 3}[/tex]
The parent function is given as:
[tex]\mathbf{f(x) = (\frac{1}{4})^x}[/tex]
From the graph, the function is shifted down by 3 units.
This means that:
[tex]\mathbf{g(x) = f(x) - 3}[/tex]
Substitute [tex]\mathbf{f(x) = (\frac{1}{4})^x}[/tex]
[tex]\mathbf{g(x) = (\frac{1}{4})^x - 3}[/tex]
Hence, the function on the graph is: [tex]\mathbf{g(x) = (\frac{1}{4})^x - 3}[/tex]
Read more about function transformations at:
https://brainly.com/question/13810353
