Graph-to-Table Matching: Analyzing Two-Segment Linear Graph in Coordinate Plane

Q: How do I read coordinates accurately from a graph?

Start at your point and trace straight down to the x-axis to find the x-coordinate, then trace straight left or right to the y-axis for the y-coordinate. Count grid squares carefully!

Q: What if the line doesn't pass through perfect grid points?

Look for the points where the line does cross grid intersections clearly. These are usually the key points the question wants you to identify. Don't worry about points between grid lines.

Q: Why does this graph have two different line segments?

This is called a piecewise function - it has different behaviors in different intervals. The first segment is horizontal (constant y-value), then it changes to a downward slope.

Q: How do I know which table is correct?

Find all the clear coordinate points from the graph first. Then check each table option - only one will have exactly those same coordinate pairs in the same order.

Piecewise Linear Functions with Table Matching

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

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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

00:06 We'll take a specific X value and find the corresponding Y value according to the graph

00:12 We'll place each point in the table

00:17 And that's the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

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

Step-by-step solution

To find the table corresponding to the graph, let's proceed step-by-step:

Step 1: Identify points from the graph.
Step 2: Deduce the coordinates by examining the graph.
Step 3: Compare these coordinates to those listed in the choices.

Step 1: Observing the graph, it passes through the following points: $(-3,1)$ , $(0,1)$ , and $(3,0)$ .

Step 2: We deduce these points by checking intersections where the line crosses a visible grid point.

Step 3: Now, compare these points to the tables given in the options:

Choice 1: Matches $(-3,1)$ , $(0,1)$ , $(3,0)$ .
Choice 2, 3, and 4: Do not match these points based on given coordinates.

Therefore, the table that matches the graph's data points is Choice 1.

The correct table according to the graph is: $\begin{array}{|c|c|c|}\hline X & -3 & 0 & 3 \\ \hline Y & 1 & 1 & 0 \\ \hline \end{array}$

Final Answer

Key Points to Remember

Essential concepts to master this topic

Graph Reading: Identify key points where line changes direction or crosses axes
Coordinate Extraction: At x = -3, y = 1; at x = 0, y = 1; at x = 3, y = 0
Verification: Check that all three points from graph match exactly in chosen table ✓

Common Mistakes

Avoid these frequent errors

Reading coordinates incorrectly from graph
Don't estimate or guess coordinate values from the visual appearance = wrong table selection! Grid intersections can be deceiving without careful counting. Always trace from each point directly to both axes and count grid units precisely.

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 read coordinates accurately from a graph?

Start at your point and trace straight down to the x-axis to find the x-coordinate, then trace straight left or right to the y-axis for the y-coordinate. Count grid squares carefully!

What if the line doesn't pass through perfect grid points?

Look for the points where the line does cross grid intersections clearly. These are usually the key points the question wants you to identify. Don't worry about points between grid lines.

Why does this graph have two different line segments?

This is called a piecewise function - it has different behaviors in different intervals. The first segment is horizontal (constant y-value), then it changes to a downward slope.

How do I know which table is correct?

Find all the clear coordinate points from the graph first. Then check each table option - only one will have exactly those same coordinate pairs in the same order.

What if two tables seem close but have slight differences?

Even small differences matter! Mathematical relationships must be exact. Double-check your coordinate reading from the graph - there should be one table that matches perfectly.

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