given the function f (x) = g (x-3) - 2, describe transformation of f (x) on a coordinate plane relative to g (x).

f (x) is obtained by translate g (x) 3 units to the right and 2 units down

Step-by-step explanation:

* Lets talk about the transformation of a function

- If the function f (x) translated horizontally to the right

by h units, then the new function g (x) = f (x - h)

- If the function f (x) translated horizontally to the left

by h units, then the new function g (x) = f (x + h)

- If the function f (x) translated vertically up

by k units, then the new function g (x) = f (x) + k

- If the function f (x) translated vertically down

by k units, then the new function g (x) = f (x) - k

* Lets study the problem and solve it

∵ f (x) = g (x - 3) - 2

- x-coordinate change from x to x - 3, that means

# x-coordinate is translated 3 units to the right

- y-coordinate change from y to y - 2, that means

# y-coordinate is translated 2 units down

∴ The transformation is:

translated 3 units to the right and 2 units down

* f (x) is obtained by translate g (x) 3 units to the right and 2 units down