Problems from Bounded functions

Determine if the following functions are bounded:

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

  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 $$x = 0$$.

imagen

Solution:

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