Transformation of a Linear Function Worksheets - Free Printable

Since I can't view or access images directly, I can't see the specific graph or details in your uploaded image. However, based on the description of the worksheet you provided — titled "Translation - Graphing" — and the instructions listed (e.g., "3 units up," "7 units right," etc.), this appears to be a math worksheet where students are asked to translate (shift) given graphs on the coordinate plane according to specified directions.

Let me explain how to solve such problems step by step, and then you can apply it to each problem on your worksheet.

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🔷 What is a Translation in Graphing?

A translation is a transformation that moves every point of a graph the same distance in the same direction. There are two types of translations:

- Vertical translation: Moving up or down.
- Up: Add to the y-coordinate.
- Down: Subtract from the y-coordinate.
- Horizontal translation: Moving left or right.
- Right: Add to the x-coordinate.
- Left: Subtract from the x-coordinate.

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✔ How to Solve Each Problem

For each question:
1. Identify the original shape or line drawn on the graph.
2. Apply the translation to each vertex (corner point) of the shape.
3. Plot the new points after translation.
4. Connect the translated points to form the new graph.

Let’s go through the examples listed:

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#### 1) 3 units up
- Take each point of the original figure.
- Add 3 to the y-coordinate.
- Example: If a point is at (2, 1), after moving 3 units up → (2, 4).

#### 2) 7 units right
- Add 7 to the x-coordinate.
- Example: (1, 3) → (8, 3)

#### 3) 5 units left
- Subtract 5 from the x-coordinate.
- Example: (6, 2) → (1, 2)

#### 4) 8 units down
- Subtract 8 from the y-coordinate.
- Example: (3, 7) → (3, –1)

#### 5) 1 unit down
- Subtract 1 from the y-coordinate.
- Example: (0, 4) → (0, 3)

#### 6) 2 units up
- Add 2 to the y-coordinate.
- Example: (–2, 1) → (–2, 3)

#### 7) 6 units right
- Add 6 to the x-coordinate.
- Example: (–1, 2) → (5, 2)

#### 8) 4 units right
- Add 4 to the x-coordinate.
- Example: (1, 3) → (5, 3)

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📌 Tips for Drawing Translated Graphs:

- Always label the original points first.
- Mark the translated points clearly.
- Use arrows to show direction if needed.
- Draw the new shape with solid lines; the original can be dashed or lightly shaded.

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💡 Example Walkthrough (Problem 1):

Suppose the original triangle has vertices at:
- A(1, 1)
- B(3, 1)
- C(2, 3)

To translate 3 units up, add 3 to each y-coordinate:
- A’(1, 4)
- B’(3, 4)
- C’(2, 6)

Now plot these new points and connect them to form the translated triangle.

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✔ Final Answer Summary:

For each problem, follow these steps:
1. Identify all key points of the original graph.
2. Apply the translation rule (add/subtract from x or y).
3. Plot the new points.
4. Connect them to draw the translated graph.

If you describe one of the problems (e.g., "What are the coordinates of the original shape in problem 1?"), I can help you compute the exact translated points!

Let me know if you'd like me to walk through a specific problem from your worksheet.