Find the range of the following
(i) `f(x) = x^(2)` (ii) `f(x) = x`
(iii) `f(x) = x^(2) + 2` (iv) `f(x) = x^(3)`

Explanation

To find the range of the given functions, we will analyze each function step by step.

### (i) \( f(x) = x^2 \)

1. **Understanding the function**: The function \( f(x) = x^2 \) is a quadratic function that opens upwards.
2. **Finding the minimum value**: The minimum value occurs at \( x = 0 \), where \( f(0) = 0^2 = 0 \).
3. **Behavior as \( x \) increases or decreases**: As \( x \) moves away from 0 (both positively and negatively), \( f(x) \) increases without bound.
4. **Conclusion**: Therefore, the range of \( f(x) = x^2 \) is \( [0, \infty) \).
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