Even, Odd, or Neither Functions Card Sort Activity (Digital and Print) - Free Printable

Since I can't view or access images directly, I’ll help you solve the Even, Odd, or Neither Graph Quiz based on the description of the task and typical content of such quizzes.

🔍 Task Overview:

You are given a set of functions and graphs. For each function or graph, determine whether it is:
- Even (symmetric about the y-axis),
- Odd (symmetric about the origin), or
- Neither.

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✔ Definitions:

A function $ f(x) $ is:
- Even: if $ f(-x) = f(x) $ → symmetric about the y-axis
- Odd: if $ f(-x) = -f(x) $ → symmetric about the origin
- Neither: if it doesn’t satisfy either condition

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Let’s go through each function and graph one by one.

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📌 Part 1: Functions (Algebraic)

We'll test each function using $ f(-x) $.

#### 1. $ f(x) = x^3 - x $
- $ f(-x) = (-x)^3 - (-x) = -x^3 + x = -(x^3 - x) = -f(x) $
- ✔ Odd

#### 2. $ f(x) = 7x^2 + 5 $
- $ f(-x) = 7(-x)^2 + 5 = 7x^2 + 5 = f(x) $
- ✔ Even

#### 3. $ f(x) = x^3 - 2 $
- $ f(-x) = (-x)^3 - 2 = -x^3 - 2 \neq f(x) $, and $ \neq -f(x) $
- ✘ Neither

#### 4. $ f(x) = x^4 - 4x^2 $
- $ f(-x) = (-x)^4 - 4(-x)^2 = x^4 - 4x^2 = f(x) $
- ✔ Even

#### 5. $ f(x) = x^3 - 3x^2 $
- $ f(-x) = (-x)^3 - 3(-x)^2 = -x^3 - 3x^2 \neq f(x) $, $ \neq -f(x) $
- ✘ Neither

#### 6. $ f(x) = 5x + 3 $
- $ f(-x) = -5x + 3 \neq f(x) $, $ \neq -f(x) $
- ✘ Neither

#### 7. $ f(x) = -7x $
- $ f(-x) = -7(-x) = 7x = -(-7x) = -f(x) $
- ✔ Odd

#### 8. $ f(x) = -2x^3 $
- $ f(-x) = -2(-x)^3 = -2(-x^3) = 2x^3 = -(-2x^3) = -f(x) $
- ✔ Odd

#### 9. $ f(x) = 4x^3 $
- $ f(-x) = 4(-x)^3 = -4x^3 = -f(x) $
- ✔ Odd

#### 10. $ f(x) = 4x $
- $ f(-x) = -4x = -f(x) $
- ✔ Odd

#### 11. $ f(x) = 5x^2 - x + 1 $
- $ f(-x) = 5(-x)^2 - (-x) + 1 = 5x^2 + x + 1 \neq f(x) $, $ \neq -f(x) $
- ✘ Neither

#### 12. $ f(x) = -x^4 $
- $ f(-x) = -(-x)^4 = -x^4 = f(x) $
- ✔ Even

#### 13. $ f(x) = -5x - 3 $
- $ f(-x) = -5(-x) - 3 = 5x - 3 \neq f(x) $, $ \neq -f(x) $
- ✘ Neither

#### 14. $ f(x) = -x^3 + 1 $
- $ f(-x) = -(-x)^3 + 1 = x^3 + 1 \neq f(x) $, $ \neq -f(x) $
- ✘ Neither

#### 15. $ f(x) = 2x^3 $
- $ f(-x) = 2(-x)^3 = -2x^3 = -f(x) $
- ✔ Odd

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📈 Part 2: Graphs

Now, analyze the graphs based on symmetry.

> Since I can't see the image, I will describe how to interpret common graph types:

#### Graph 1: Straight line passing through origin with positive slope
- Example: $ y = x $
- Symmetric about origin → Odd

#### Graph 2: V-shaped graph (absolute value)
- Example: $ y = |x| $
- Symmetric about y-axis → Even

#### Graph 3: Parabola opening up, vertex at origin
- Example: $ y = x^2 $
- Symmetric about y-axis → Even

#### Graph 4: Cubic curve passing through origin, increasing
- Example: $ y = x^3 $
- Symmetric about origin → Odd

#### Graph 5: Line not through origin (e.g., $ y = x + 1 $)
- Not symmetric about y-axis or origin → Neither

#### Graph 6: Wavy graph (like cosine wave) symmetric about y-axis
- Example: $ y = \cos(x) $
- Symmetric about y-axis → Even

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✔ Final Answers (Based on Common Patterns)

Assuming the graphs are standard ones:

| Function / Graph | Answer |
|------------------|--------|
| $ f(x) = x^3 - x $ | Odd |
| $ f(x) = 7x^2 + 5 $ | Even |
| $ f(x) = x^3 - 2 $ | Neither |
| $ f(x) = x^4 - 4x^2 $ | Even |
| $ f(x) = x^3 - 3x^2 $ | Neither |
| $ f(x) = 5x + 3 $ | Neither |
| $ f(x) = -7x $ | Odd |
| $ f(x) = -2x^3 $ | Odd |
| $ f(x) = 4x^3 $ | Odd |
| $ f(x) = 4x $ | Odd |
| $ f(x) = 5x^2 - x + 1 $ | Neither |
| $ f(x) = -x^4 $ | Even |
| $ f(x) = -5x - 3 $ | Neither |
| $ f(x) = -x^3 + 1 $ | Neither |
| $ f(x) = 2x^3 $ | Odd |

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📊 Graphs (Typical Interpretations):

| Graph | Description | Even/Odd/Neither |
|-------|-------------|------------------|
| 1 | Line through origin, slope >0 | Odd |
| 2 | V-shape (like |x|) | Even |
| 3 | Parabola opening up, vertex at origin | Even |
| 4 | Cubic curve through origin | Odd |
| 5 | Line not through origin | Neither |
| 6 | Wave symmetric about y-axis | Even |

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💡 Tips for Identifying:

- Even: Flip over y-axis → same graph.
- Odd: Rotate 180° around origin → same graph.
- Neither: Doesn’t satisfy either.

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If you can describe the graphs (e.g., “a parabola shifted right,” or “a cubic going down then up”), I can give more specific answers!

Let me know if you want this formatted as a table or printable answer sheet.