$r(x)$ has domain $\{-1,0,1,2\}$ and range $\{0,2,4,6\}$. $s(x)$ has domain $\{1,2,3,4\}$ and is defined by $s(x)=x+1$. What is
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If you evaluate directly this function at x=0, you'll see that you have a zero denominator.
Nevertheless, the only way for a fraction to equal zero is to have a zero numerator, i.e.
So, this function can't have zeroes, because the only point that would annihilate the numerator would annihilate the denominator as well.
Moreover, we have
So, we can't even extend with continuity this function in such a way that