Bounded functions

Determine if the following functions are bounded:

  1. $f (x) = 1$
  2. $f (x) = x$
  3. $f (x) = x^2$

  1. The function is bounded.

  2. It is not bounded.

  3. Since it is a squared function, it will always be positive, therefore the function is bounded from below by $0$.

Using its graph we can observe that the function presents a minimum in $x = 0$.

  1. Bounded.
  2. Not bounded.
  3. Bounded only from bellow.
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