Answer:
Domain: (-∞, ∞)
Range: f(x) ≤ 4 or (-∞, 4]
Step-by-step explanation:
Given the quadratic function, [tex]f(x) = -2(x + 1)^{2} + 4[/tex]
where (-1, 4) is the vertex. Since the parabola is downward-facing, and its vertex is at point (-1, 4) in which it is the highest point, then it means that the value of range must be greater than or equal to 4.
Therefore, the range of the graph is:
f(x) ≤ 4 or
interval notation: (-∞, 4].
Set builder-notation: {y ∈ R | y ≤ 4}
The domain is all x values. Therefore, we can say that the domain is:
interval notation: (-∞, ∞).
Set builder-notation: {x | x ∈ R}.
