# Thread: Stuck on a STEP function about continuity.

1. ## Stuck on a STEP function about continuity.

Find the largest value of k for which the function defined by

is continuous on the interval [3, 3+k) .

...Through aproximation I found that in order to stay in one "step" the interval has to be [3, <sqrt(10)) but I can't seem to find a way to find k algebraically from the beginning.

2. Originally Posted by Arturo_026
Find the largest value of k for which the function defined by

is continuous on the interval [3, 3+k) .

...Through aproximation I found that in order to stay in one "step" the interval has to be [3, <sqrt(10)) but I can't seem to find a way to find k algebraically from the beginning.
Well
Because $\left\lfloor {3^2 - 2} \right\rfloor = 7$
we know that $x^2-2<8$
so $x^2<10$.

3. Originally Posted by Plato
Well
Because $\left\lfloor {3^2 - 2} \right\rfloor = 7$
we know that $x^2-2<8$
so $x^2<10$.
Right, then i get k < sqrt(10) - 3
Then, what would be the largest value k can attain?