Question

Gerald graphs the function f(x) = (x – 3)2 – 1. Which statements are true about the graph? Select three options.

The domain is {x| x ≥ 3}.
The range is {y| y ≥ –1}.
The function decreases over the interval (–∞, 3).
The axis of symmetry is x = –1.
The vertex is (3, –1).

Answer 1

Correct choices:
- The range is {y | y ≥ –1}.
- The function decreases over the interval (–∞, 3).
- The vertex is (3, –1).

Reason: f(x) = (x−3)^2 − 1 is an upward parabola with vertex at (3, −1), axis x = 3, domain all real numbers, range y ≥ −1, and it decreases for x < 3 and increases for x > 3.