# Is there way to know if a step function has no zeros just by its rule? Without graph

• June 9th 2013, 10:47 AM
Functionater
Is there way to know if a step function has no zeros just by its rule? Without graph
I just had a question about step functions.
Is there way to know if a step function has no zeros just by its rule? Without graphing it. Is there an equation/discriminant?

Thanks :P
• June 9th 2013, 11:20 AM
Plato
Re: Is there way to know if a step function has no zeros just by its rule? Without gr
Quote:

Originally Posted by Functionater
I just had a question about step functions.
Is there way to know if a step function has no zeros just by its rule? Without graphing it. Is there an equation/discriminant?

This is an odd question. If it is possible to determine if zero in in the range from the rule, then yes.

For example, $f(x) = \left\lfloor {{x^2}} \right\rfloor + 1$ is a step function and it has no zeros.
Because $\forall x,~f(x)>0$.