Question

1. what is the range of the graph shown below? a. -1 ≤ x ≤ 4 b. -3 ≤ x ≤ 2 c. -1 ≤ y ≤ 4 d. -3 ≤ y ≤ 2

Explanation:

Step1: Recall Range Definition

Range of a graph is the set of all possible \( y \)-values (outputs) the function can take. So we focus on the vertical (y - axis) extent of the graph.

Step2: Analyze the Graph's Vertical Extent

Looking at the graph, find the minimum and maximum \( y \)-values. The lowest point on the graph (minimum \( y \)) is at \( y = - 3 \), and the highest point (maximum \( y \)) is at \( y = 2 \)? Wait, no, wait. Wait, let's re - examine. Wait, the options: Let's check the graph again. Wait, the vertices: one at (0, - 3), one at (- 1, 0), one at (1, 4)? Wait, no, maybe I misread. Wait, the options are about \( y \)-values. Let's check the options:

Option A and B are about \( x \)-values (domain), so we can eliminate them because range is about \( y \). Now between C and D. Let's find the minimum and maximum \( y \)-coordinates of the graph. The lowest point (minimum \( y \)): looking at the graph, the vertex at the bottom is at \( y=-3 \), and the highest point (maximum \( y \)) is at \( y = 2 \)? Wait, no, wait the option D is \( - 3\leq y\leq2 \), and option C is \( - 1\leq y\leq4 \). Wait, maybe I made a mistake. Wait, let's look at the graph again. The graph has a point at (0, - 3) (the bottom), a point at (1, 4)? No, maybe the grid. Wait, the key is: range is \( y \)-values. So we need to find the minimum and maximum \( y \) on the graph.

Looking at the graph, the lowest \( y \)-value (minimum) is - 3, and the highest \( y \)-value (maximum) is 2. So the range is \( - 3\leq y\leq2 \), which is option D. Wait, but let's check the options again. Option D: \( - 3\leq y\leq2 \), option C: \( - 1\leq y\leq4 \). Wait, maybe I misread the graph. Wait, the graph: let's see the points. The left - most point is at \( x=-1,y = 0 \), the bottom point is at \( x = 0,y=-3 \), the peak is at \( x = 1,y = 4 \)? No, that can't be. Wait, maybe the graph is different. Wait, the options: Let's recall that range is the set of all \( y \)-values. So first, eliminate A and B because they are in terms of \( x \) (domain). Now, for the \( y \)-values: the minimum \( y \) is - 3 (from the bottom vertex) and the maximum \( y \) is 2? Wait, no, maybe the peak is at \( y = 2 \)? Wait, the option D is \( - 3\leq y\leq2 \), which matches the vertical extent (minimum \( y=-3 \), maximum \( y = 2 \)). Option C has minimum \( y=-1 \) and maximum \( y = 4 \), which does not match. So the correct answer is D.

Answer:

D. \( -3 \leq y \leq 2 \)