MCQ worksheet with graphs of linear equations for identifying correct representations.

Since I can't view or access images directly, I can't see the specific graph options or equations in your uploaded image. However, I can help you solve the problem if you describe the content of the image — for example:

- The equations given (e.g., \( y = |x - 2| \), \( y = -3|x| \), etc.)
- The multiple-choice graphs provided for each question
- Or simply type out the questions and answer choices

Alternatively, here’s how to approach these types of problems generally:

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Common Absolute Value Graph Questions

These questions typically ask you to match an absolute value equation to its correct graph.

#### General Rules:
1. Basic form: \( y = |x| \) is a V-shaped graph with vertex at (0,0).
2. Horizontal shift:
- \( y = |x - h| \) shifts right by \( h \) units if \( h > 0 \).
- \( y = |x + h| \) shifts left by \( h \) units.
3. Vertical shift:
- \( y = |x| + k \) shifts up by \( k \) units.
- \( y = |x| - k \) shifts down by \( k \) units.
4. Reflection & Stretch:
- \( y = -|x| \) flips the V upside down.
- \( y = a|x| \): if \( a > 1 \), it's narrower; if \( 0 < a < 1 \), it's wider.

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Let’s go through common examples:

#### Example 1: Which graph represents \( y = |x - 2| \)?
- This is a right shift of 2 units from \( y = |x| \).
- Vertex at \( (2, 0) \).
- Look for a V-shape with vertex at (2,0).

#### Example 2: Which graph represents \( y = -|x| \)?
- This is the standard V-shape flipped downward.
- Vertex still at (0,0), but opens downward.

#### Example 3: Which graph represents \( y = |x| + 3 \)?
- Standard V-shape shifted up by 3 units.
- Vertex at (0,3).

#### Example 4: Which graph represents \( y = |x + 1| - 2 \)?
- Shift left by 1, down by 2.
- Vertex at (-1, -2).

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If you provide the exact equations and describe the graphs (or list the options), I can tell you which one is correct and explain why.

Just reply with:
> "The equations are:
> 1. \( y = |x - 2| \)
> 2. \( y = -|x| \)
> 3. \( y = |x| + 3 \)
> 4. \( y = |x + 1| - 2 \)
> 5. \( y = 2|x| \)
> And the graphs are labeled A–D for each."

Then I’ll walk you through matching them!