Your question contains several points to address here. And following Martin's suggestion, it is time to wrap up the points already mentioned in comments into a conclusive answer, too.
- "IR spectrum graphs"-- there is nothing such. The graph (or, the figure) represents the IR spectrum. (And, for future reference, should there be need to deploy the plural form, it is "spectra".)
- "Are IR spectra specific to compounds or to functional groups?" If you record IR spectra in the typical interval of 4000 to 600 (or, depending on the window materials built in, about 500) 1/cm, then your IR spectrum will contain both: absorption bands that are characteristic for functional groups, like the classic ca. 1600 1/cm for carbonyls, or the ca. 2270 1/cm for the nitrile; AND between about 1400 to 500 1/cm what is called "fingerprint region" which contains absorption pattern that are characterisitic for the very molecule.
Attribution which absorption band in the fingerprint region belongs to what structural feature may be complicated enough that looking up a reference cataloge (by Sadtler, Aldrich, or other corporations) does not help, yet thankfully, modern computer chemical methods often allow a prediction of what vibrations may occur and where these should be observable in the IR spectrum. To render this fingerprint region more legible, often the $\tilde\nu$-scale is depicted with changes the scaling, like at 2200 and 1100 1/cm.
- Which of the four compounds is more likely to be the one for the spectrum depicted?
Well at first sight, 3 (1,4-dioxane) differs by the absence of a carbonyl group, typically yielding an intense absorption band around 1600 1/cm. However, such an absorption band is recorded -- so it is either acetophenone (1), cyclohexanone (2), or $\delta$-valerolactone (4).
There is not so much absorption in the region of 500--600 1/cm that were typical for aromatic rings, rendering 1 unlikely.
Now, facing the distinction between either cyclohexanon 2, or the ester 4, it is indeed helpful that these compounds are literature known, already characterized by IR spectroscopy, and -- thankfully -- their data are made public; for example by AIST. And as it turns out, it is likely cyclohexanone 2 which's spectrum was depicted here.
As a comment to the spectra by AIST: They are searchable by chemical name, formula, or CAS number. In the case of IR spectra, a little table ($\tilde\nu$), observed remnant transmittance) and a small image of the molecular structure is provided, too.
The excluded acetophenone 1:
The likely cyclohexanone 2:
The early exluded 1,4-dioxane 3:
The eventually excluded cyclic ester (lactone) 4:
So in turn, deciphering IR spectra is both learning / training to spot features (here: absorption bands), and comparison with reference data (here: spectra cataloges). And typically supported by other means of analysis or characterization, like melting points / refractive indices compared with tables, or further NMR spectroscopy, for example.
