https://file.aiquickdraw.com/mathbot/file/1727691059006wffxq543.jpg

The equation given is \( y = x^3 - 1 \). To interpret this:

1. **Equation Analysis**: This equation describes a cubic function. For each value of \( x \), the output \( y \) is determined by cubing \( x \) and subtracting 1.
   
2. **Table of Values**:
   The table provided shows the following pairs of values:
   \[
   \begin{array}{c|c}
   x & y \\
   \hline
   2 & 7 \\
   1 & 0 \\
   0 & -1 \\
   -1 & -2 \\
   -2 & -9 \\
   \end{array}
   \]

   These values are correct based on the equation:
   \[
   y = x^3 - 1
   \]
   For example:
   - For \( x = 2 \): \( y = 2^3 - 1 = 8 - 1 = 7 \)
   - For \( x = 1 \): \( y = 1^3 - 1 = 1 - 1 = 0 \)
   - For \( x = 0 \): \( y = 0^3 - 1 = 0 - 1 = -1 \)
   - For \( x = -1 \): \( y = (-1)^3 - 1 = -1 - 1 = -2 \)
   - For \( x = -2 \): \( y = (-2)^3 - 1 = -8 - 1 = -9 \)

3. **Graphing the Function**:
   The blank grid on the left can be used to plot the points \((x, y)\) from the table:
   \[
   (2, 7), (1, 0), (0, -1), (-1, -2), (-2, -9)
   \]
   You would mark these points on the grid and connect them to show the cubic curve.

4. **Is this a function?**:
   Yes, this is a function. Each value of \( x \) corresponds to exactly one value of \( y \), meaning it passes the vertical line test (a vertical line would intersect the graph at only one point).

Would you like a more detailed explanation or help with graphing?

---

### Additional Questions:
1. What is the general shape of a cubic function on a graph?
2. How does the vertical line test work to determine if something is a function?
3. Can a function have the same output for different inputs?
4. How would the graph of \( y = x^3 - 1 \) differ from \( y = x^3 \)?
5. What is the significance of the constant term \(-1\) in the equation \( y = x^3 - 1 \)?

### Tip:
When graphing cubic functions, note that they usually have an "S" shape, with one end going to positive infinity and the other to negative infinity.

Is y = x^3 - 1 a function? Graph the following points.

Learn how to graph the cubic function y = x^3 - 1 by plotting points like (2, 7), (1, 0), and others. Understand key concepts like cubic equations and the vertical line test to determine if it's a function.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation