Question

give the domain and range of the graph shown to the right. then, use the graph to answer parts (a) through (d) below. the domain of the graph to the right is -3,3. (type your answer in interval notation.) the range of the graph to the right is -2,2. (type your answer in interval notation.) a. find f(-3). f(-3)= -2 b. find f(0). f(0)=

Explanation:

Step1: Locate x=0 on graph

Find the point where \( x = 0 \) on the given graph.

Step2: Determine y - value at x=0

The graph has a point at \( x = 0 \). From the graph, when \( x = 0 \), the corresponding \( y \) - value (which is \( f(0) \)) can be seen. Looking at the graph, the vertex (the point where the two line segments meet) is at \( x = 0 \), and the \( y \) - coordinate of that point is 0? Wait, no, let's re - examine. Wait, the left segment goes from \( (-3,-2) \) to \( (0,0) \)? Wait, no, looking at the grid: the leftmost point is \( (-3,-2) \), then it goes to \( (0,0) \)? Wait, no, the graph: the first segment is from \( (-3,-2) \) (since at \( x=-3 \), \( y = - 2 \)) to \( (0,0) \)? Wait, no, the middle point (the corner) is at \( x = 0 \). Let's check the coordinates. The x - axis and y - axis: each grid square is 1 unit. So at \( x = 0 \), the \( y \) - value is 0? Wait, no, maybe I made a mistake. Wait, the left point is \( (-3,-2) \), then the line goes to \( (0,0) \), then from \( (0,0) \) to \( (3,2) \)? Wait, no, the rightmost point is at \( x = 3 \), \( y = 2 \)? Wait, the problem's graph: the left end is at \( (-3,-2) \), then a line to \( (0,0) \) (the corner), then a line to \( (3,2) \). So when \( x = 0 \), the \( y \) - value is 0? Wait, no, let's count the grid. The y - axis: from - 6 to 6. The point at \( x = 0 \): looking at the graph, the corner is at \( (0,0) \)? Wait, no, maybe the corner is at \( (0,0) \). So \( f(0)=0 \)? Wait, no, let's check the coordinates again. The left point: \( x=-3 \), \( y = - 2 \) (since it's 3 units left of the origin on the x - axis and 2 units down on the y - axis). Then the line goes to \( (0,0) \) (0 on x, 0 on y), then from \( (0,0) \) to \( (3,2) \) (3 units right, 2 units up). So when \( x = 0 \), \( y = 0 \), so \( f(0)=0 \)? Wait, but maybe I misread. Wait, the original problem's graph: the user's graph: the leftmost point is \( (-3,-2) \), then a line to \( (0,0) \) (the vertex), then a line to \( (3,2) \). So at \( x = 0 \), \( f(0)=0 \). Wait, but let's confirm. The domain is \( [-3,3] \), range is \( [-2,2] \). For part (a), \( f(-3)=-2 \), which matches the leftmost point. For part (b), \( x = 0 \), so we look at the graph at \( x = 0 \). The point at \( x = 0 \) is the vertex, and its \( y \) - coordinate is 0. So \( f(0)=0 \).

Answer:

\( 0 \)