Determine if the following functions are bounded:
- $$f (x) = 1$$
- $$f (x) = x$$
- $$f (x) = x^2$$
See development and solution
Development:
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The function is bounded.
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It is not bounded.
- 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 $$x = 0$$.
Solution:
- Bounded.
- Not bounded.
- Bounded only from bellow.