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

Answer 1

• The range is y ≥ –1.
• The function decreases over the interval (–∞, 3).
• The vertex is (3, –1).

Explanation:

You want to find the true statements describing the graph of f(x) = (x -3)² -1.

Vertex form

The function is written in vertex form:

f(x) = a(x -h)² +k . . . . . . . vertex (h, k)

Comparing to this form, we see the vertex is

(h, k) = (3, -1)

The value of "a" is 1, so the graph opens upward. This means it is decreasing for x-values less than 3, It also means the range is upward from -1.

• The range is y.
• The function decreases over the interval (–∞, 3).
• The vertex is (3, –1).