Question

identify the domain and range of the quadratic graph provided below. options: $-3 < x < 0$, $-3 leq x leq 0$, $-4 < y < 0$, $-4 leq y leq 0$

Explanation:

Step1: Determine the Domain

The domain of a graph is the set of all x - values for which the graph exists. Looking at the quadratic graph, the leftmost point is at \(x=-3\) (with a closed dot, indicating inclusion) and the rightmost point is at \(x = 0\) (also with a closed dot, indicating inclusion). So the domain is all real numbers \(x\) such that \(-3\leq x\leq0\).

Step2: Determine the Range

The range of a graph is the set of all y - values for which the graph exists. The lowest point of the graph (since it's a downward - opening parabola) has a y - value of \(-4\) (closed dot, included) and the highest point (the vertex) has a y - value of \(0\) (included, as the vertex is on the x - axis). So the range is all real numbers \(y\) such that \(-4\leq y\leq0\).

Answer:

Domain: \(\boldsymbol{-3\leq x\leq0}\)
Range: \(\boldsymbol{-4\leq y\leq0}\)