June 26, 2019

### Bounded from Above

A function is **bounded above** if there is a real number,** k**, such that for all of **x**, **f(x) ≤ k**.

The number **k** is called the **upper bound**.

** k = 0.135**

### Bounded from Below

A function is **bounded below** if there is a real number,** k'**, such that for all of **x**, **f(x) ≥ k′**.

The number **k'** is called the **lower bound**.

**k′ = 2**

### Bounded Function

**k′**** ≤ f(x) ≤ k**

**k = ½ k′ = -½**

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