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The question is asking you to use the graph of the function \( y = 3\sqrt{x} - 1 \) to find the solutions to the equation \( -2 = 3\sqrt{x} - 1 \).

To solve the equation \( -2 = 3\sqrt{x} - 1 \) algebraically:

### Step-by-step solution:

1. **Start with the equation:**
   \[
   -2 = 3\sqrt{x} - 1
   \]

2. **Add 1 to both sides to isolate the square root term:**
   \[
   -2 + 1 = 3\sqrt{x}
   \]
   \[
   -1 = 3\sqrt{x}
   \]

3. **Divide both sides by 3:**
   \[
   \frac{-1}{3} = \sqrt{x}
   \]

4. **This is where the problem arises:**
   The square root of a number cannot be negative. Since \( \sqrt{x} \) cannot be negative, there is **no solution** to this equation.

Thus, the solution to the equation is that no solution exists. You would enter "DNE" (Does Not Exist) as the solution.

Would you like any further details or explanations on this?

Here are 5 related questions to explore:

1. How do you graph the function \( y = 3\sqrt{x} - 1 \)?
2. Can an equation with a square root have negative solutions?
3. How do you solve other types of radical equations?
4. What are the domain restrictions for square root functions?
5. How does the graph of \( y = 3\sqrt{x} - 1 \) compare to \( y = \sqrt{x} \)?

**Tip:** Always consider the domain of a function when solving equations, especially those involving square roots!

Use a graph of y = 3√x - 1 to determine the solutions to the equation -2 = 3√x - 1. If there is more than one solution, separate the values with a comma. If there are no solutions, enter DNE for Does Not Exist.

This problem explains how to solve the radical equation -2 = 3√x - 1 by graphing the function y = 3√x - 1. Learn why the solution does not exist due to square root properties and domain restrictions. Suitable for high school students in Grades 9-12.

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