Bounded Functions

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.

Bounded from Above

 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.

Bounded from Below

k′ = 2

Bounded Function

k′ ≤ f(x) ≤ k

Bounded Function

 k = ½        k′ = -½