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 $y = 0$).