The function f (x) = 2x is translated left 3 units and down 2 units. Which is the equation of the translated function?

g (x) = 22 - 3 - 2

g (x) = 2x-2-3

g (x) = 2x - 2 + 3

g (x) = 2x + 3_2

g (x) = 2 (x+3) - 2

Step-by-step explanation:

At first we should know the rules of translation

1) {f (x) + a} is f (x) shifted up (a) units

2) {f (x) - a} is f (x) shifted down (a) units

3) {f (x + a) } is f (x) shifted left (a) units.

4) {f (x - a) } is f (x) shifted right a units.

So, The function f (x) = 2x is translated left 3 units and down 2 units

Applying the rules (2) and (3)

∴f (x) ⇒ f (x+3) - 2 = 2 (x+3) - 2

∴ g (x) = 2 (x+3) - 2

g (x) = 2x + 3 - 2