Question

If the original function f(x) = 2x2 - 1 is shifted to the left 3 units to make the function g(x), which expression would represent g(x)?

(1)2(x-3)^2-1 (3)2x^2+2
(2)2(x+3)^2-1 (4)2x^2-4​

Answer 1

Answer: 2(x+3)^2 - 1

To shift the f(x) function 3 units to the left, the xy axis must move 3 units to the right. This effectively means each x input is 3 units larger than before. That's why we replace every x with x+3.