Gerald graphs the function f (x) = (x - 3) 2 - 1. Which statements are true about the graph? Check all that apply.

The domain is x.

The range is y.

The function decreases over the interval (-∞, 3).

The function increases over the interval (-1, ∞).

The axis of symmetry is x = - 1.

The vertex is (3, - 1).

second third and sixth

Statement 1 is false because the domain of f is all real numbers since the function is quadratic.

Statement 2 is true.

Statement 3 is true because when we graph f, it is a parabola opening upwards with vertex (3, - 1). Since it is opening upward, then the value of x from - ∞ to 3 is decreasing while increasing from 3 to ∞.

Statement 4 is false because we just stated above that f is decreasing from - ∞ to 3. Hence, f is also decreasing from - 1 to 3. Hence, f is not increasing from - 1 to ∞.

Statement 5 is false because the axis of symmetry is x = 3.

Statement 6 is true.