Question

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

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

Answer 1

To obtain the translated function g(x) of f(x) = 2x, which is shifted left by 3 units and down by 2 units, the equation is g(x) = 2(x + 3) - 2.

Step-by-step explanation:

The function f(x) = 2x is translated left 3 units and down 2 units to obtain a new function g(x). To translate the function to the left by 3 units, we replace x with (x + 3) because the function f(x - d) represents a translation to the right by d units, so f(x + d) translates it to the left. To then translate the function down by 2 units, we subtract 2 from the entire expression. Therefore, the equation of the translated function is g(x) = 2(x + 3) - 2.