You don't necessarily have to focus only on an FPTAS, and not even on positive results. The key idea is an approximation-preserving reduction: if you reduce problem A to problem B, then an $\alpha$-approximation algorithm for B implies a $f(\alpha)$-approximation for A, where $f$ is some function. Now observe both of the following are true: if A is hard to approximate, so is B. Also, if you can approximate B, you can also approximate A.
For example, consider an instance $(G,k)$ of chromatic number. Suppose there is a polynomial-time algorithm that, given $(G,k)$, constructs an instance $(G',k')$ of problem X. Moreover, suppose it holds that the size of $G'$ is linear in the size of $G$, $k' = k$, and $(G,k)$ is a YES-instance of chromatic number iff $(G',k')$ is a YES-instance of X. Now, any algorithm approximating problem X is also an approximation algorithm for chromatic number. But in fact, it is known chromatic number cannot be approximated within a factor of $n^{1-\varepsilon}$ for any $\varepsilon > 0$ (unless P = NP). Thus, the same is true for problem X.