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

To shift a graph to the left, you must subtract a value from x.

g(x) = x^2 − 3
The entire graph is subtracted by 3, so the graph moves down.

g(x) = x^2 + 3
The entire graph is added by 3, so the graph moves up.

g(x) = (x + 3)^2
The x value is added by 3, so the graph moves to the right.

The answer is g(x) = (x + 3)^2, because the addition of 3 to the x value moves the graph to the left.