# Boundedness

### Topic Page

Boundedness### Questions

- What is boundedness?
- What are some examples of bounded functions?
- Are all functions bounded?
- How does the boundedness of a function relate to its graph?
- What are some examples of unbounded functions?
- Is #y = 5# an upper bound for #f(x) = x^2 + 5#?
- What is the boundedness theorem?
- Is there a lower bound for #f(x) = 5 - 1/(x^2)#?
- Can an absolute value have a discontinuity #f(x)= |x-9| / (x-9)#?
- Suppose #I# is an interval and function #f:I->R# and #x in I# . Is it true that #f(x)=1/x# is not bounded function for #I=(0,1)# ?. How do we prove that ?