Linear Piecewise Function: Match Graph to Corresponding Table

Given the following graph, determine which table corresponds to the following table

To solve this problem, we will follow these steps:

• Step 1: Examine the graph and identify the points that stand out on the graph.
• Step 2: Analyze the coordinates of these points by looking at the $X$ and $Y$ axes.
• Step 3: Compare these coordinates to the provided table choices.

Now, let's go through each step in detail:

Step 1: Upon examining the graph, it depicts a piecewise linear graph passing through several key points. Notably, there's a horizontal segment and a slanted segment forming a "V" shape. Consider the points where the line changes direction or intersects with an axis.

Step 2: Looking closely, we can identify three main points from the graph: - At $x = -4$, $y = -1$. - At $x = 0$, $y = -1$. - At $x = 4$, $y = 3$.

Step 3: Next, we compare these coordinates to the options provided as tables:

1. Choice 1 suggests points $(x,y): (1,3), (2,4), (3,5)$ which does not match our graph.
2. Choice 2 has $(x,y): (-1,3), (0,4), (1,7)$ which also does not fit the described graph.
3. Choice 3 presents $(x,y): (-4,-1), (0,-1), (4,3)$ which exactly matches all the observed points from our examination of the graph!
4. Choice 4 offers $(x,y): (0,3), (2,4), (4,5)$ which again is not comparable with the graph.

Thus, upon reviewing all the choices, we determine that the correct table corresponding to the graph is Choice 3.

Therefore, the solution to the problem is Choice 3.