Question

Graph each transformation, g(x) and write the equation for the transformed functionI don't quite understand these questions and my teacher didn't explain these too well

Answer 1

1) Let's graph each transformation, considering the parent function, i.e. the simplest version of the same function

$\begin{gathered} f(x)\text{ = }4^{x-1} \\ g(x)=\text{ }f(x)-2 \end{gathered}$

2) Let's plot then, considering that:

• f(x) is the parent function

,

• The second function is translated horizontally 2 units down since it's outside the parentheses.

,

• We need to make a table for that:

x | y=4^(x-1)

1 |1 (1,1)

2| 4 (2,4)

3 |16 (3,6)

g(x) =4^(x-1) - 2

x| y

1 | -1 (1,-1)

2 | 2 (2,2)

3 | 14 (3,14)

And we can see this graph like this, in red f(x) and two units down the blue one g(x)