Question

The graph of f(x) = x^2 is shifted 3 units to the left to obtain the graph of g(x). Which of the following equations best describes g(x)?

g(x) = (x + 3)^2
g(x) = x^2 − 3
g(x) = x^2 + 3
g(x) = (x − 3)^2

Answer 1

Shifting a graph 3 units to the left means that you will add 3 to the value of x before applying the exponent.

The graph of x^2 − 3 would be shifted 3 units down.
The graph of x^2 + 3 would be shifted 3 units up.
The graph of (x − 3)^2 would be shifted 3 units to the right, because the x value is subtracted by 3 to make the shift to the right.

The answer is 'g(x) = (x + 3)^2'.