Match the equation with the graph it defines.

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y = sqrt(x)	a. l6001sqrt

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y = x^2 	b. l6001recip

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y = x^3	c. l6001x3

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y = abs(x)	d. l6001absx

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y = 1/x	e. l6001x2

The task is to match each equation with the label of the graph it defines. Let's go through each equation and match it with the appropriate graph:

1. **\( y = \sqrt{x} \)**  
   This equation represents the square root function, a curve that starts at the origin (0,0) and rises gradually as x increases.  
   **Match:** \( l6001sqrt \) (a)

2. **\( y = x^2 \)**  
   This is the equation of a parabola, a U-shaped curve that opens upwards and is symmetric around the y-axis.  
   **Match:** \( l6001x2 \) (e)

3. **\( y = x^3 \)**  
   This equation represents a cubic function, which has an S-shaped curve that passes through the origin and increases sharply on both sides.  
   **Match:** \( l6001x3 \) (c)

4. **\( y = |x| \)**  
   The absolute value function forms a V-shaped graph, which also passes through the origin. It reflects all negative values of x to positive y-values.  
   **Match:** \( l6001absx \) (d)

5. **\( y = \frac{1}{x} \)**  
   This is the reciprocal function, which has two branches, one in the first quadrant and another in the third quadrant. The graph approaches the x- and y-axes but never touches them.  
   **Match:** \( l6001recip \) (b)

### Final Matching:
- \( y = \sqrt{x} \) → \( l6001sqrt \) (a)
- \( y = x^2 \) → \( l6001x2 \) (e)
- \( y = x^3 \) → \( l6001x3 \) (c)
- \( y = |x| \) → \( l6001absx \) (d)
- \( y = \frac{1}{x} \) → \( l6001recip \) (b)

Would you like any further details or clarification?

### Related Questions:
1. What are the domain and range of \( y = \sqrt{x} \)?
2. How does the graph of \( y = x^2 \) change if we modify it to \( y = -x^2 \)?
3. Can you explain the symmetry properties of \( y = x^3 \) and \( y = |x| \)?
4. What happens to the graph of \( y = \frac{1}{x} \) as \( x \to 0 \)?
5. How do horizontal and vertical shifts affect these functions?

**Tip:** To better understand a function’s graph, try plotting it and observing key features such as intercepts, asymptotes, and symmetry.

Match the equation with the graph it defines.

Learn how to match equations such as y = sqrt(x), y = x^2, y = x^3, y = |x|, and y = 1/x with their corresponding graphs. This problem involves key algebraic concepts and graph behavior, making it suitable for students in Grades 9-12.

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