I have a McBook Pro since 2007. Can I view my screen on the TV using the Apple TV 3rd generation that I just purchased?

AirPlay Mirroring requires a second-generation Apple TV or later, OS X 10.8 or better and is supported on the following Mac models: iMac (Mid 2011 or newer), Mac mini (Mid 2011 or newer), MacBook Air (Mid 2011 or newer), and MacBook Pro (Early 2011 or newer). You can see which Mac you have and which operating system you are using by selecting 'About this Mac' from the Apple menu in the top left corner of your Mac and selecting the 'More Info' button.

There are some 3rd party products such as AirParrot etc, but in testing I've found them pretty unreliable.