Absolute Value Equations Color by Number - Free Printable

It looks like you've uploaded a worksheet with multiple graphs labeled A through L, each showing a piecewise linear graph on the coordinate plane. Each graph has a color label (e.g., Teal, Blue, Black, etc.), and it seems like the task might be to identify transformations or match functions based on their shapes.

However, the actual problem statement is missing — there's no question or instruction provided in the image. Common tasks for such worksheets include:

- Identifying which graphs are reflections, translations, or dilations of others.
- Matching equations to graphs.
- Determining which graphs represent absolute value functions or other specific forms.
- Grouping graphs by shape or transformation.

Since no explicit question is given, I’ll analyze the graphs and provide a detailed breakdown so we can solve any potential task.

---

🔍 Step-by-step Analysis of Graphs

We will describe each graph’s key features: vertex, direction, symmetry, and general shape.

#### A. Teal
- V-shaped, opening upward.
- Vertex at (2, 0).
- Left side: from (2,0) to (-4,6), slope = (6-0)/(-4-2) = 6/-6 = -1.
- Right side: from (2,0) to (5,3), slope = (3-0)/(5-2) = 3/3 = 1.
- This resembles $ y = |x - 2| $, but scaled? Let's check:
- At x=1: y=1 → |1-2|=1 ✔
- At x=3: y=1 → |3-2|=1 ✔
- But at x=-4: y=6 → |-4-2|=6 ✔
- So yes, this is $ y = |x - 2| $.

#### B. Blue
- V-shaped, but inverted (downward), then up again?
- Points: (0,5), (1,-2), (2,5)
- From (0,5) to (1,-2): slope = -7
- From (1,-2) to (2,5): slope = 7
- Symmetric around x=1, vertex at (1,-2)
- Looks like $ y = 7|x - 1| - 2 $? Wait: at x=0: 7(1)-2 = 5 ✔; x=2: 7(1)-2=5 ✔
- So: $ y = 7|x - 1| - 2 $

#### C. Black
- V-shaped, opening upward.
- Vertex at (1,0)
- Left: (1,0) to (-4,5): slope = (5-0)/(-4-1) = 5/-5 = -1
- Right: (1,0) to (5,5): slope = (5-0)/(5-1) = 5/4 ≠ 1 → not symmetric
Wait: (1,0) to (5,5): slope = 5/4 → not same as left side.

But wait: let’s plot points:
- From (-4,5) to (1,0): Δx=5, Δy=-5 → slope = -1
- From (1,0) to (5,5): Δx=4, Δy=5 → slope = 5/4

Not symmetric → not a standard absolute value function.

But visually, it's a "V" pointing up, vertex at (1,0), but arms have different slopes.

So likely not an absolute value function.

Wait — maybe it's just two lines meeting at (1,0). Not symmetric.

Let’s compare to A: A has symmetric slopes ±1. C does not.

So C is not a standard absolute value.

But look closely: from (-4,5) to (1,0): slope = -1
From (1,0) to (5,5): slope = 5/4 → not symmetric.

So C is not a reflection of A.

But notice: A has vertex at (2,0), C at (1,0)

Hmm.

Let’s skip ahead.

#### D. Pink
- V-shaped, vertex at (1,0)
- Left: (1,0) to (0,5): slope = (5-0)/(0-1) = 5/-1 = -5
- Right: (1,0) to (2,5): slope = (5-0)/(2-1) = 5
- So symmetric, slopes ±5 → $ y = 5|x - 1| $

Yes! $ y = 5|x - 1| $

#### E. Black
- V-shaped, vertex at (-2,0)
- Left: (-2,0) to (-5,-5): slope = (-5-0)/(-5+2) = -5/-3 = 5/3
- Right: (-2,0) to (1,-5): slope = (-5-0)/(1+2) = -5/3
- So symmetric about x=-2, slopes ±5/3 → $ y = \frac{5}{3}|x + 2| $, but downward?

Wait: y-values go down → negative coefficient.

At vertex (-2,0), goes down → so $ y = -\frac{5}{3}|x + 2| $

Yes.

#### F. Orange
- V-shaped, vertex at (-3,0)
- Left: (-3,0) to (-6,-3): slope = (-3-0)/(-6+3) = -3/-3 = 1
- Right: (-3,0) to (0,-3): slope = (-3-0)/(0+3) = -3/3 = -1
- So symmetric, slopes ±1, but both going down → $ y = -|x + 3| $

Yes.

#### G. Green
- V-shaped, vertex at (2,0)
- Left: (2,0) to (1,6): slope = (6-0)/(1-2) = 6/-1 = -6
- Right: (2,0) to (3,6): slope = 6/1 = 6
- So symmetric → $ y = 6|x - 2| $

#### H. Yellow
- V-shaped, vertex at (2,3)
- Left: (2,3) to (1,-2): slope = (-2-3)/(1-2) = -5/-1 = 5
- Right: (2,3) to (3,-2): slope = (-2-3)/(3-2) = -5/1 = -5
- So symmetric, slopes ±5 → $ y = -5|x - 2| + 3 $

Because it opens downward, vertex at (2,3).

#### I. Orange
- V-shaped, vertex at (1,1)
- Left: (1,1) to (0,-5): slope = (-5-1)/(0-1) = -6/-1 = 6
- Right: (1,1) to (2,-5): slope = (-5-1)/(2-1) = -6/1 = -6
- So symmetric, slopes ±6 → $ y = -6|x - 1| + 1 $

#### J. Purple
- V-shaped, vertex at (-3,0)
- Left: (-3,0) to (-6,3): slope = (3-0)/(-6+3) = 3/-3 = -1
- Right: (-3,0) to (0,3): slope = (3-0)/(0+3) = 3/3 = 1
- So symmetric, slopes ±1 → $ y = |x + 3| $

#### K. Blue
- Not V-shaped. It's a single line segment with a kink?
- Points: (-3,-5), (2,0), (4,-1)
- From (-3,-5) to (2,0): slope = (0+5)/(2+3) = 5/5 = 1
- From (2,0) to (4,-1): slope = (-1-0)/(4-2) = -1/2
- So not symmetric, not absolute value. Just two connected lines.

#### L. Black
- V-shaped, vertex at (0,-2)
- Left: (0,-2) to (-3,-5): slope = (-5+2)/(-3-0) = -3/-3 = 1
- Right: (0,-2) to (3,-5): slope = (-5+2)/(3-0) = -3/3 = -1
- So symmetric, slopes ±1 → $ y = -|x| - 2 $

Wait: at x=0, y=-2 → correct.
At x=3: y = -|3| - 2 = -5 ✔
At x=-3: same → -5 ✔
So: $ y = -|x| - 2 $

---

Summary of Functions

| Label | Color | Function |
|-------|---------|---------------------------|
| A | Teal | $ y = |x - 2| $ |
| B | Blue | $ y = 7|x - 1| - 2 $ |
| C | Black | Not standard (asymmetric) |
| D | Pink | $ y = 5|x - 1| $ |
| E | Black | $ y = -\frac{5}{3}|x + 2| $ |
| F | Orange | $ y = -|x + 3| $ |
| G | Green | $ y = 6|x - 2| $ |
| H | Yellow | $ y = -5|x - 2| + 3 $ |
| I | Orange | $ y = -6|x - 1| + 1 $ |
| J | Purple | $ y = |x + 3| $ |
| K | Blue | Not absolute value |
| L | Black | $ y = -|x| - 2 $ |

---

Possible Tasks & Solutions

Since the actual question is missing, here are common possibilities and how to solve them:

---

#### 🟩 Task 1: Match graphs that are transformations of each other

For example:
- A and J: Both have slope ±1, but different vertices.
- A: $ y = |x - 2| $
- J: $ y = |x + 3| $
- These are horizontal shifts: A is right by 2, J is left by 3.

- D and G: Both have steeper slopes.
- D: $ y = 5|x - 1| $
- G: $ y = 6|x - 2| $
- Different steepness and shift.

- B and H: Both have vertex at x=1 or x=2, but different forms.
- B: $ y = 7|x - 1| - 2 $
- H: $ y = -5|x - 2| + 3 $
- No direct relation.

- F and J:
- F: $ y = -|x + 3| $
- J: $ y = |x + 3| $
- So F is reflection of J over x-axis.

✔ So F and J are reflections of each other.

Similarly:
- L and A:
- A: $ y = |x - 2| $
- L: $ y = -|x| - 2 $
- Not related directly.

But J and F are reflections.

Also:
- G and D:
- G: $ y = 6|x - 2| $
- D: $ y = 5|x - 1| $
- Different scales and shifts.

---

#### 🟨 Task 2: Identify which graphs are absolute value functions

All except C, K are absolute value functions (or piecewise linear with V-shape).

- C: Asymmetric — not absolute value.
- K: Not V-shaped — just two segments.

So C and K are NOT absolute value functions.

---

#### 🟦 Task 3: Find which graphs are reflections over the x-axis

Look for pairs where one is the negative of the other.

- J: $ y = |x + 3| $
- F: $ y = -|x + 3| $ → reflection of J over x-axis.

✔ So F is reflection of J

- H: $ y = -5|x - 2| + 3 $
- Is there a positive version? Look at G: $ y = 6|x - 2| $ → different scale.

No direct match.

- I: $ y = -6|x - 1| + 1 $
- D: $ y = 5|x - 1| $ → not same.

So only F and J are reflections.

---

#### 🟪 Task 4: Which graphs have the same shape?

Same shape means same slope magnitude and orientation.

- A and J: both have slope ±1, but different locations.
- D and G: D has slope ±5, G has ±6 → different.
- E and L: E has slope ±5/3, L has ±1 → different.

But A and J have same slope magnitude → same "steepness" and shape.

So A and J are congruent in shape (just shifted).

Similarly, D and G are similar but not same scale.

---

✔ Final Answer (Assuming Common Task)

If the task is: "Which pair of graphs are reflections of each other?"

Then the answer is:
👉 F (Orange) and J (Purple)

Because:
- F: $ y = -|x + 3| $
- J: $ y = |x + 3| $
- They are reflections over the x-axis.

---

If the task is: "Which graphs are not absolute value functions?"

Then:
👉 C and K

Because:
- C: asymmetric V → not absolute value
- K: not V-shaped → not absolute value

---

If the task is: "Identify the graph of $ y = |x + 3| $"

Then:
👉 J (Purple)

---

If the task is: "Which graph represents $ y = -|x| - 2 $"

Then:
👉 L (Black)

---

📌 Conclusion

Without the exact question, the most likely intended task is:

> "Which two graphs are reflections of each other over the x-axis?"

Answer: F (Orange) and J (Purple)

✔ Because they are negatives of each other: $ y = |x + 3| $ and $ y = -|x + 3| $

---

If you can provide the actual question from the worksheet (e.g., "Match the graphs", "Find reflections", "Identify the equation", etc.), I can give a more precise answer.

But based on standard problems like this, the key insight is recognizing reflections and transformations of absolute value functions.

Let me know if you'd like to match equations or find specific transformations!