Question

The graph of a quadratic function with vertex (-2, 3) is shown in the figure below.
Find the domain and the range.
Write your answers as inequalities, using r or y as appropriate.
Or, you may instead click on "Empty set" or "All reals" as the answer.

Answer 1

Answer:

Domain:   -∞ < x < ∞

Domain in interval notation: (-∞ , ∞ )

Range: f(x) ≤ 3

Range in interval notation: (-∞ , 3]

Step-by-step explanation:

Given the quadratic function where the vertex occurs at point (-2, 3) as the maximum point on the graph:

Domain

The domain does not have any horizontal restrictions in terms of the input values. Thus, we could express the domain as:

Domain: - ∞ < x < ∞

Domain in interval notation: (-∞ , ∞ )

Range

Since the graph opens downward, the maximum y-value is 3, as defined by the vertex, (-2, 3).  Therefore, we could express the range of the function as:

Range: f(x) ≤ 3

Range in interval notation: (-∞ , 3]