Question

identify the domain and range of the quadratic graph provided below
domain :
range :
options: $-1 < x < 3$, $-1 \leq x \leq 3$, $-3 \leq y < 5$, $-3 < y \leq 5$

Explanation:

Step1: Analyze Domain

The graph has open circles at \( x = -1 \) and \( x = 3 \)? Wait, no, looking at the graph, the left end has an open circle at \( x=-1 \) (y=2) and the right end has an open circle at \( x = 3 \) (y=5)? Wait, no, the domain is the set of x - values. The graph is a parabola segment. The leftmost x - value is \( x=-1 \) (open circle, so not included) and the rightmost x - value is \( x = 3 \) (open circle, so not included)? Wait, no, wait the options: the first option is \( -1 - 1 \), and the right end is an open circle at \( x = 3 \), so \( x<3 \). So domain is \( -1 - 1 \)) and right boundary is \( x = 3 \) (open, so \( x<3 \)), so domain is \( -1

Step2: Analyze Range

Range is the set of y - values. The lowest point of the parabola (vertex) is at y=-3 (closed? Wait the vertex is at (let's see, the graph has a minimum at y=-3, and the open circles at y=2 (left) and y=5 (right). Wait the y - values: the minimum y is - 3 (since the vertex is at y=-3, and the graph includes that point? Wait the vertex is a closed point? Wait the graph: the parabola has a minimum at y=-3, and the open circles are at the top. So the y - values: the minimum y is - 3 (included, since the vertex is part of the graph) and the maximum y is less than 5 (since the top points are open circles at y=5, so y < 5). Wait the options for range: third option is \( -3\leq y<5 \), fourth is \( -3

Wait let's re - check:

Domain: x - values. The graph starts at x > - 1 (open circle at x=-1) and ends at x < 3 (open circle at x=3), so domain is \( -1

Range: y - values. The minimum y is - 3 (the vertex, which is included, so \( y\geq - 3 \)) and the maximum y is less than 5 (since the top points are open circles, so \( y < 5 \)), so range is \( -3\leq y<5 \).

Answer:

Domain: \( -1 < x < 3 \) (option: \( -1Range: \( -3\leq y<5 \) (option: \( -3\leq y<5 \))

Wait, but let's check the options again. The options are:

1. \( -1
2. \( -1\leq x\leq3 \)
3. \( -3\leq y<5 \)
4. \( -3

So for domain, the correct option is the first one (\( -1