Mesa, zone R-9 is residential, single family, lots of at least 9000 sq ft.
Keeping of livestock (such as chickens) on a lot less than 35,000 sq ft (as yours is) requires a Special Use Permit. No guarantees they will issue one (judging from the rest of the code, it seems highly likely they won't. (11-31-4) Even less likely a rooster would be permitted.
Tempe, zoning R1-7, R1-6 allow the keeping of small livesstock with a special use permit and significant restrictions in those zones (limit 5 total, no roosters or peafowl, no on site processing, others). Additionally, you must conform to any overlay district requirements, if applicable. (Rio Salado District, SW Tempe District, Historic District, etc)
Chandler, zoning SF8.5 will allow limited chickn keeping by permit, no roosters. You need to check overlay districts as well.
Simple. Look up the code, read. Your real estate agent should be able to do this for you, but better you learn to do it yourself - so you don't buy a property having told your realtor you want to be able to have chickens, only to find that you can't.
Those are all relatively small properties for chicken ownership, I'm not surprised roosters are prohibited, and the rest is by special use only.
/edit and generally speaking, if you want a rooster (or chickens at all, in many places), you want either an AG district or an RA (Residential/Ag) border district, where they exist.
I live in FL, looked up your codes on my cell phone, and have no specific knowledge of AZ - I've driven few a few times, that is all.