Using a MacBook air as a monitor
Yep, 


Plug your iPhone into your MacBook via Lightning-to-USB cable.
Open QuickTime Player (it's on every Mac)
While QuickTime Player is running, click File in the menu bar.
Select "New Movie Recording" (not "New Screen Recording" like one may think)
Click the arrow on the right of the record button to open a dropdown
Select your iPhone under the camera section
If you want sound as well, repeat 5 &amp; 6, but select your iPhone under "Microphone", as well


That's it! Your iPhone will have to be within USB cable length of your Mac, but you will be able to see everything on it that you will be able to see on your iPhone, and it's 100% free.

Note: mirroring the screen of your iPhone on your Mac will drain the battery life substantially