Linear Piecewise Function: Match Graph to Corresponding Table

Q: How do I know which points are most important on a piecewise graph?

Look for points where the graph changes direction or has corners, plus any intercepts with the axes. These critical points define the shape of your piecewise function.

Q: What if the graph seems to pass through points between the grid lines?

Focus on points that clearly land exactly on grid intersections. These give you precise coordinates. If a point seems between lines, look more carefully or check nearby integer coordinates.

Q: Should I check every point on the line or just a few key ones?

Check the key transition points where segments meet and any clear intercepts. For this type of problem, 3-4 well-chosen points are usually enough to identify the correct table.

Q: What if two tables seem close but not exactly right?

The correct table must match all the key points exactly. Even if one coordinate is off, that table is incorrect. Piecewise functions require precise coordinate matching.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Choose the appropriate table for the graph

00:03 We want to find points on the graph, and place them in the table

00:08 We'll take a specific X value and find the corresponding Y value according to the graph

00:14 We'll place each point in the table

00:24 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

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

2

Step-by-step solution

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:

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

3

Final Answer

Key Points to Remember

Essential concepts to master this topic

Graph Reading: Identify key points where line segments meet or change direction
Technique: Check coordinates at x = -4, y = -1; x = 0, y = -1; x = 4, y = 3
Verification: Match all three coordinate pairs from graph to table entries ✓

Common Mistakes

Avoid these frequent errors

Reading only one or two points from the graph
Don't just identify the endpoints and ignore transition points = missing key coordinates! This leads to choosing incorrect tables that only partially match. Always identify all critical points including corners, intersections, and direction changes.

Practice Quiz

Test your knowledge with interactive questions

Determine whether the following table represents a constant function:

FAQ

Everything you need to know about this question

How do I know which points are most important on a piecewise graph?

+

Look for points where the graph changes direction or has corners, plus any intercepts with the axes. These critical points define the shape of your piecewise function.

What if the graph seems to pass through points between the grid lines?

+

Focus on points that clearly land exactly on grid intersections. These give you precise coordinates. If a point seems between lines, look more carefully or check nearby integer coordinates.

Should I check every point on the line or just a few key ones?

+

Check the key transition points where segments meet and any clear intercepts. For this type of problem, 3-4 well-chosen points are usually enough to identify the correct table.

How can I tell if my coordinates are correct?

+

Start from the origin and count grid squares carefully. Move right for positive x, left for negative x, up for positive y, and down for negative y. Double-check each coordinate pair.

What if two tables seem close but not exactly right?

+

The correct table must match all the key points exactly. Even if one coordinate is off, that table is incorrect. Piecewise functions require precise coordinate matching.

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Linear Piecewise Function: Match Graph to Corresponding Table

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