Find range of a reciprocal function given domain

Question

I cannot find the range of this reciprocal function: 1/(x+1) whose domain is {x:x≥0, x a real number}.

I could draw the graph of this function but my confusion is if x-values are getting bigger from 0, then y-values are getting closer to 0 or approaching infinity, which means y-values are not getting bigger as x-values get bigger. Then how do I write the range?

Thanks in advance.

Answer 1

The $y$ values cannot approach $\infty$, the maximum value of $y$ is $1$ when $x=0$. As you say the function decreases, approaching $0$ but not getting there, so the range is $(0,1]$