rogeriodec
Amazingly, my headphones have a better frequency response that Tapco monitors, especially in deep bass.
As you can see, the response starts to get fairly flat only after 100hz.
This is terrible!
Now I wonder, should I throw these audio monitors in the trash?

No, don't throw them out. It's not entirely your monitors' fault. 
 
Any speaker will have a minimum frequency that it can correctly reproduce. It's a physical limitation based on the natural resonant frequency of the speaker itself and the enclosure it's in. Low-frequency response can be aided somewhat by the enclosure design, e.g. porting, but ultimately it's a hard limit dictated by physics.
 
The room you're in is a critical part of the system, too, along with the speaker and its enclosure. Small rooms have the worst problems, but almost any room will be less than flat due to resonances. Even if you trashed the Tapcos and mortgaged your house to buy high-end mastering speakers, you would still not measure a flat frequency response because the room would still impose its own acoustical fingerprint.
 
And it gets worse...your room's frequency response isn't static, it changes over time. I don't mean years, but milliseconds. Some frequencies ring out longer than others, which makes it even harder to adjust your EQ, and smears the image. It's the reason "room EQ" solutions such as ARC only get you part way there. Get a copy of Room EQ Wizard and use it to create a waterfall graph, which is similar to the graph you made except it shows multiple measurements over time.
 
Adding acoustic absorbers will help flatten the room response, although getting them to solve low-frequency problems is expensive. A small investment will, however, smooth response in the mids and highs and help mitigate ringing. 
 
Absorption won't help the biggest problem revealed by your graph, though, which is simply lack of response below 70 Hz. There is no cure other than upgrading your speaker system. The cheapest and easiest solution would be to add a subwoofer for around $400. It's either that or replace your speakers, but that'll cost you $1500-2000 for a significant upgrade.
 

It's perhaps worth remembering that most of the systems the "public" (for want of a better word) use to listen to music are pretty poor performers in the bass region. Mixing on a system that's a bit bass-light can actually result in a more transferable mix. If all your bass impact is down below 80Hz or thereabouts lots of reproduction systems just can't reproduce it accurately if at all.

Getting an accurate frequency plot from a monitor is a bit more complicated than putting a microphone in front of it as well. What matters is the frequency response at a reasonable listening distance because speakers don't transmit all frequncies in all directions. Higher frequencies principally come from the centre of the cone, so a close mic on the centre has less bass. Conversly a close mic at the speaker edge tends to have more bass, less of whatever the speaker's maximum treble frequencies happen to be. This is why guitar speakers can sound so radically different as you move a mic around them.

Then there's the issue of the tweeter vs the woofer. Tweeters tend to be searchlight-like in terms of dispersion so a mic too close to the woofer won't pick up much of their output at all. Assuming white noise as a test audio source, the frequency plot posted has a stunning drop-off in the treble for example - either there's something going on with the tweeter/cross-over design or the test mic wasn't picking it up either because of placement or maybe phasing effects between the speakers in the monitor. If that treble drop-off is genuine I'd be more concerned about that than the bass roll-off to be honest. A mix that compensates for it could be unpleasantly bright on other systems.

The closest thing to an "industry standard" measurement system is to place the speaker in either an anocheic chamber or a huge space so reflections from walls etc. aren't a factor then to take measurements using a specialist measurement mic that itself has a pretty flat - and known, so it can be compensated for - frequency response.

What matters is frequency response at the listening position in the room you're in. And even then "flat" may not be desirable. Human hearing isn't "flat response", hi-fi speakers and headphones aren't "flat response" and people don't live in echo-free empty spaces. And lots of consumer earbuds/headphones artificially boost bass up a lot anyway, so a slightly bass-light mix might even transfer better to those.

There's also an argument that a heightened mid response can be useful when mixing. The Yamaha NS10 was a very popular and successful near-field in its day, and it had an awful frequency response plot. No bass, not much top, shedloads of squawking mid. It just so happened that lots of people found them really good for making transferable mixes that sounded good to OK on pretty much any playback equipment - a lot of engineers and producers reckoned "If it sounds good on NS10s it'll sound good on anything".

If you're mixing/mastering anticipating playback through club PA systems, then yes, you do need to lnow what the sub-sub-bass might be doing. But then you'll also probably be mixing in mono and hoping the club PA is installed well enough not to create huge phasing issues.