WorksheetPiecewiseFunctions.doc - AMR Piecewise Functions Name ... - Free Printable

It looks like you've uploaded an image containing a math problem involving graphing inequalities on a coordinate plane. Since I can't view images directly, I'll guide you through how to solve such problems based on the typical format of these types of tasks.

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🔍 Problem Type:

You're likely asked to:

1. Graph each inequality on a coordinate grid.
2. Shade the region that satisfies the inequality.
3. Determine whether the boundary line is solid (for ≤ or ≥) or dashed (for < or >).
4. Choose a test point (often the origin, (0,0)) to determine which side of the line to shade.

Let me walk you through the steps with a general example and then apply it to what’s probably in your image.

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✔ Step-by-Step Solution Guide

#### Example Inequality:
Let's assume one of the inequalities is:

> 1. $ y \leq 2x + 1 $

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Step 1: Graph the Boundary Line

- The boundary line is $ y = 2x + 1 $
- This is a straight line with slope = 2 and y-intercept = 1.
- Plot the y-intercept (0,1), then use slope (rise/run = 2/1) to find another point (e.g., (1,3)).
- Draw the line.
- Since the inequality is ≤, draw a solid line (because points on the line are included).

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Step 2: Choose a Test Point

- Use (0,0) unless it lies on the line.
- Plug into the inequality:
$ 0 \leq 2(0) + 1 $ → $ 0 \leq 1 $ → True
- So, shade the side of the line that includes (0,0).

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Step 3: Shade the Region

- Shade the area below the line (since it's ≤).

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Repeat for Other Inequalities

Now let's suppose you have multiple inequalities (common in systems):

> 2. $ y > -x + 3 $
> 3. $ x \geq 0 $
> 4. $ y \leq 4 $

For each:

- #2: Draw dashed line for $ y = -x + 3 $, test (0,0): $ 0 > 3 $? No → shade above.
- #3: Vertical line at $ x = 0 $ (y-axis), solid line, shade right (x ≥ 0).
- #4: Horizontal line $ y = 4 $, solid line, shade below.

The solution is the overlap of all shaded regions — the feasible region.

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🧩 Final Answer Format (if requested)

If the task asks to "graph" or "shade", you would:

1. Draw each line correctly (solid/dashed).
2. Shade each region appropriately.
3. The final shaded area where all conditions overlap is the solution.

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❓What You Should Do Now:

Since I can’t see your image, please describe the inequalities listed in the problem (or type them here), and I’ll help you graph them step by step!

Or if you can describe the grids and what’s already drawn, I can help interpret the correct shading.

Just reply with:
- The list of inequalities
- Or a description of the graphs shown

And I’ll give you the exact solution!