The function 1x2 is always positive, and it increases without bound as x gets close to 0 and decreases toward zero as x gets bigger and bigger (whether positive or negative.)
You might know its graph:
graph{y=1/x^2 [-14.06, 14.42, -3.99, 10.25]}
Now in this question, the function is f(x)=5−1x2.
Starting with 5, we will subtract 1x2 which is a number greater than 0, but with no upper bound.
That means at for some x we will subtract 500, and for some other x we will subtract 5,000 and for another subtract 60,000 from 5. (We will never subtract a negative, because 1x2 is never negative.)
The result of this subtraction will be at most 5 but for very large positive 1x2, we will get very 'big' negatives, like −100 and then −10,000 and so on.
So, there is no lower bound for f.
Upper bounds
f(x) is bounded above (by every number greater than or equal to 5) but is not bounded below. 5 is the least upper bound.
