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.