Find domain and range of following function: `y=x^(3)`

Explanation

To find the domain and range of the function \( y = x^3 \), we can analyze the function step by step.

### Step 1: Identify the function
The function given is \( y = x^3 \). This is a polynomial function.

### Step 2: Determine the domain
The domain of a function is the set of all possible input values (x-values) that the function can accept.

- Since \( y = x^3 \) is a polynomial function, it is defined for all real numbers.
- There are no restrictions on the values of \( x \) (like square roots or denominators that could be zero).

Thus, the domain of \( y = x^3 \) is:
\[ \text{Domain} = (-\infty, +\infty) \]

### Step 3: Determine the range
The range of a function is the set of all possible output values (y-values) that the function can produce.

- As \( x \) takes on all real values, \( y = x^3 \) will also take on all real values.
- For very large positive values of \( x \), \( y \) will also be very large and positive.
- For very large negative values of \( x \), \( y \) will be very large and negative.

Thus, the range of \( y = x^3 \) is:
\[ \text{Range} = (-\infty, +\infty) \]

### Conclusion
The domain and range of the function \( y = x^3 \) are both all real numbers:
- **Domain:** \( (-\infty, +\infty) \)
- **Range:** \( (-\infty, +\infty) \)

---