Function table worksheet for plotting linear equations on coordinate grids.

It looks like you've uploaded a worksheet titled "Function Table" that includes several problems where students are asked to:

1. Complete the function table for given functions.
2. Plot the points on a coordinate grid.
3. Draw the graph of the function.

Since I can't view images directly, I’ll walk you through how to solve this type of problem step by step based on the typical format of such worksheets. Let’s assume the worksheet contains six problems (numbered 1–6), each with a function rule like $ f(x) = 2x $, and a table with input ($ x $) values and blank output ($ f(x) $) values.

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🔧 General Steps to Solve Each Problem

#### Step 1: Understand the Function Rule
Each problem gives a function rule, such as:
- $ f(x) = 2x $
- $ f(x) = x + 4 $
- $ f(x) = -x $

You'll use this rule to calculate the output ($ f(x) $) for each input ($ x $).

#### Step 2: Fill in the Function Table
For each $ x $ value, plug it into the function and compute $ f(x) $.

#### Step 3: Plot the Points
Use the $ (x, f(x)) $ pairs as coordinates and plot them on the graph provided.

#### Step 4: Draw the Graph
Connect the points with a straight line (if linear) or draw the appropriate curve.

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Let me now go through each problem as they typically appear on such worksheets. Since I don’t have the exact image, I’ll reconstruct what likely appears based on common patterns.

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✔ Problem 1: $ f(x) = 2x $

| $ x $ | $ f(x) $ |
|--------|-----------|
| 0 | 0 |
| 1 | 2 |
| 2 | 4 |
| 3 | 6 |

✔ Graph: Plot points (0,0), (1,2), (2,4), (3,6). Draw a straight line through them.

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✔ Problem 2: $ f(x) = x + 4 $

| $ x $ | $ f(x) $ |
|--------|-----------|
| 0 | 4 |
| 1 | 5 |
| 2 | 6 |
| 3 | 7 |

✔ Graph: Plot (0,4), (1,5), (2,6), (3,7). Line with slope 1, y-intercept 4.

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✔ Problem 3: $ f(x) = -x $

| $ x $ | $ f(x) $ |
|--------|-----------|
| 0 | 0 |
| 1 | -1 |
| 2 | -2 |
| 3 | -3 |

✔ Graph: Points (0,0), (1,-1), (2,-2), (3,-3). Line with negative slope.

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✔ Problem 4: $ f(x) = -x + 4 $

| $ x $ | $ f(x) $ |
|--------|-----------|
| 0 | 4 |
| 1 | 3 |
| 2 | 2 |
| 3 | 1 |

✔ Graph: Points (0,4), (1,3), (2,2), (3,1). Line decreasing, y-intercept 4.

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✔ Problem 5: $ f(x) = 4 - 2x $

| $ x $ | $ f(x) $ |
|--------|-----------|
| 0 | 4 |
| 1 | 2 |
| 2 | 0 |
| 3 | -2 |

✔ Graph: Points (0,4), (1,2), (2,0), (3,-2). Slope = -2, y-intercept 4.

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✔ Problem 6: $ f(x) = 2x $

Wait — this might be repeated. But let's suppose it's $ f(x) = 2x - 2 $ or similar.

But if it's again $ f(x) = 2x $, then same as Problem 1.

Alternatively, maybe it's $ f(x) = x^2 $? But since all graphs are straight lines, likely all are linear.

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📌 Key Tips:

- Always check the function rule carefully.
- Use the table to generate ordered pairs.
- Plot points accurately on the grid.
- Draw a smooth line through the points (for linear functions).
- Label axes and include arrows if needed.

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✔ Final Answer Summary:

For each problem:

1. Complete the table using $ f(x) = \text{rule} $.
2. Plot the points $ (x, f(x)) $.
3. Draw the graph — straight line for linear functions.

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If you can describe one specific problem from the image (e.g., "Problem 1: $ f(x) = 3x - 1 $, with $ x = 0, 1, 2, 3 $" and so on), I can give you the exact completed table and instructions for plotting.

Alternatively, if you want me to simulate the solution for a specific problem, just tell me the function and inputs!

Would you like me to generate a completed version of one of these problems?