List the intercepts of the equation yequalsx cubed minus 1.

To find the intercepts of the equation \( y = x^3 - 1 \), we need to determine both the **x-intercepts** and the **y-intercept**.

### 1. **Y-intercept:**

The y-intercept occurs when \( x = 0 \).

Substitute \( x = 0 \) into the equation:

\[
y = (0)^3 - 1 = -1
\]

So, the y-intercept is at the point \( (0, -1) \).

### 2. **X-intercepts:**

The x-intercepts occur when \( y = 0 \).

Set \( y = 0 \) and solve for \( x \):

\[
0 = x^3 - 1
\]
\[
x^3 = 1
\]
\[
x = \sqrt[3]{1} = 1
\]

So, the only x-intercept is at the point \( (1, 0) \).

### Final Answer:
- **Y-intercept:** \( (0, -1) \)
- **X-intercept:** \( (1, 0) \)

Would you like further details or explanations? 

Here are 5 questions that build on this information:
1. What are the intercepts of the equation \( y = x^2 - 4 \)?
2. How do you find the intercepts of a quadratic equation?
3. Can an equation have more than one y-intercept?
4. What do the intercepts tell us about the graph of a function?
5. What are the x-intercepts of the equation \( y = x^4 - 16 \)?

**Tip:** When solving for intercepts, always set the opposite variable to zero (for y-intercept, set \( x = 0 \); for x-intercepts, set \( y = 0 \)).

List the intercepts of the equation y equals x cubed minus 1.

Learn how to find the intercepts of the equation y = x^3 - 1 with a detailed step-by-step solution. This guide covers core algebraic concepts and techniques for identifying x and y intercepts, ideal for students in Grades 9-10.

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