Write the function in its final position fx x3 first moved 2

Write the function in its final position. f(x) x^3 first moved 2 units downward, then 3 units to the left and finally flipped over the y-axis. (be careful with this one, watch the order) f(x) = (x - 3)^3 -2 f(x) = (-(x -3))^3 -2 f(x) = - (x + 3)^3 -2 f(x) = (x^3 + 3) -2

Solution

The given function is f(x)=x³. First it moves towards 2 units downwards. So we get f(x)= x³-2 . Then 3 units to the left. So we get f(x)= (x+3)³-2. And finally flipped over the y-axis which give us f(x)=-(x+3)³ -2.

Hence the correct option is C