Question

what are the domain and range of the function?
domain: (-∞, ∞); range: f(x) ≥ -7
domain: (-∞, ∞); range: f(x) ≥ 7
domain: f(x) ≥ 1; range: f(x) ≥ -7
domain: f(x) ≥ 1; range: (-∞, ∞)
done

Explanation:

Step1: Recall Domain/Range Concepts

For a function (likely quadratic, as range involves \( f(x) \geq -7 \)), domain of polynomials (like quadratics) is all real numbers (\( (-\infty, \infty) \)). Range of a parabola opening up: minimum value is vertex y - coordinate. If vertex y is -7, range is \( f(x) \geq -7 \).

Step2: Analyze Options

• First option: Domain \( (-\infty, \infty) \), Range \( f(x) \geq -7 \) → matches polynomial (e.g., \( y = x^2 -7 \)) domain (all reals) and range (since it opens up, minimum at \( y=-7 \)).
• Second option: Range \( f(x) \geq 7 \) → incorrect if vertex is -7.
• Third/Fourth: Domain as \( f(x) \geq 1 \) → wrong, domain is for x - values, not f(x).

Answer:

A. domain: \( (-\infty, \infty) \); range: \( f(x) \geq -7 \) (assuming the first option is labeled A, with the text "domain: \( (-\infty, \infty) \); range: \( f(x) \geq -7 \)")