Question

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 ≥ –1.
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).

Answer 1

second third and sixth

Answer 2

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.