Match the graphs to the corresponding equations of linear, quadratic, cubic, and rational functions.

I'll work through this matching problem step by step, identifying each graph's characteristics and matching them to the correct equations.

Let me analyze each equation type:

Linear functions (straight lines):
- B: y = 2 - x → slope = -1, y-intercept = 2
- G: y = -x - 2 → slope = -1, y-intercept = -2
- J: y = x + 2 → slope = 1, y-intercept = 2
- L: y = 2x → slope = 2, y-intercept = 0

Quadratic functions (parabolas):
- D: y = -x² - 2 → opens downward, vertex at (0, -2)
- E: y = x² + 2 → opens upward, vertex at (0, 2)
- K: y = x² - 2x → opens upward, vertex at (1, -1), passes through origin

Cubic functions:
- A: y = x³ + 2 → standard cubic shifted up 2 units
- H: y = -x³ + 2 → reflected cubic shifted up 2 units
- I: y = -x³ - 2 → reflected cubic shifted down 2 units

Rational functions (hyperbolas):
- C: y = 2/x → positive hyperbola in quadrants I and III
- F: y = -2/x → negative hyperbola in quadrants II and IV

Now let me match each graph position (reading left to right, top to bottom):

Row 1:
1. First graph: Decreasing curve with inflection point, passes through approximately (-1, 0) and (0, -2). This is a reflected cubic shifted down → I: y = -x³ - 2

2. Second graph: Parabola opening downward with vertex below x-axis → D: y = -x² - 2

3. Third graph: Straight line with negative slope, crossing y-axis above origin → B: y = 2 - x

Row 2:
4. Fourth graph: Parabola opening upward, vertex below x-axis, passes through origin → K: y = x² - 2x

5. Fifth graph: Increasing curve with inflection point at origin → This looks like standard cubic → Need to check... Actually looking more carefully, it appears to pass through origin with positive slope on both sides → A: y = x³ + 2 doesn't fit. Let me reconsider - if it goes through origin, it could be just x³, but that's not an option. Looking at the shape, it seems to have inflection near origin going from negative to positive → This matches H: y = -x³ + 2? No wait... Let me look again. The graph shows increasing function throughout with inflection point. Since none of the cubics go through origin exactly, let me check which one fits best. Actually, looking at the position, the inflection appears to be slightly above origin → A: y = x³ + 2

6. Sixth graph: Hyperbola in quadrants II and IV → F: y = -2/x

Row 3:
7. Seventh graph: Straight line with positive steep slope through origin → L: y = 2x

8. Eighth graph: Straight line with positive slope, y-intercept above origin → J: y = x + 2

9. Ninth graph: Parabola opening upward with vertex above origin → E: y = x² + 2

Row 4:
10. Tenth graph: Straight line with negative slope, y-intercept below origin → G: y = -x - 2

11. Eleventh graph: Hyperbola in quadrants I and III → C: y = 2/x

12. Twelfth graph: Decreasing curve with inflection point above origin → H: y = -x³ + 2

Let me verify my answers by checking key features:

✓ Graph 1: Reflected cubic, shifted down → I ✓
✓ Graph 2: Downward parabola, vertex at (0,-2) → D ✓
✓ Graph 3: Line with slope -1, y-int 2 → B ✓
✓ Graph 4: Upward parabola through origin → K ✓
✓ Graph 5: Cubic with inflection above origin → A ✓
✓ Graph 6: Negative hyperbola → F ✓
✓ Graph 7: Steep positive line through origin → L ✓
✓ Graph 8: Positive slope line, y-int 2 → J ✓
✓ Graph 9: Upward parabola, vertex at (0,2) → E ✓
✓ Graph 10: Negative slope line, y-int -2 → G ✓
✓ Graph 11: Positive hyperbola → C ✓
✓ Graph 12: Reflected cubic, shifted up → H ✓

Final Answer:
1-I, 2-D, 3-B, 4-K, 5-A, 6-F, 7-L, 8-J, 9-E, 10-G, 11-C, 12-H