T-X

The T-X Terminatrix, one of Skynet's most advanced Terminator units, was sent back in time to July 24, 2004. Her primary mission was to terminate John Connor. Since he lived off the grid, the Terminatrix focused instead on terminating Connor's future officers of the Resistance.

Personality
The T-X appears to possess a limited emotional range, which it exhibits even when it is alone, as opposed to displaying emotion to ingratiate itself with humans. This can be seen during the crane chase when it exhibits frustration and also performs a surprised double-take upon realizing the T-850 is still in pursuit. The T-X appears to exhibit a fear response just before the T-850 finally terminates it with one of his hydrogen cores and manages to reform part of its human face with its remaining mimetic polyalloy to make a horrified face while trying to escape. Also, early in the film when it identifies blood as belonging to "primary target" John Connor, the T-X appears to react with an expression akin to a gasp of excitement.

The T-X is also the only machine to make feral growling noises when angered or frustrated.

Terminator 3: Eyes of the Rise
In 2032, the T-X was battle-tested by Skynet against several other Terminators and by Skynet itself. The T-1002 engaged the Terminatrix in hand to hand combat in the Skynet Central Core, using its mimetic polyalloy components to develop stabbing weapons all across its body. The T-X was able to gain the advantage through a combination attack utilizing her internal buzz saw to remove the spikes and later destroyed T-1002 with a direct impact from her plasma cannon.

Terminator 3: Rise of the Machines
The Terminatrix arrived in July 24, 2004, in a clothes shop with mannequins, melting them and a glass frame on arrival. It then walked out of the shop, approaching a confused woman, admiring her car before killing her and taking her belongings. The Terminatrix then went on to killing any of John Connor's future lieutenants, including Kate Brewster and her father Robert Brewster. However, when she coincidentally found Connor, who had been formerly untraceable due to "living off the grid", she made him her priority target.

At the Cyber Research Systems facility, the Terminatrix obtained an Airforce uniform and injected nanobots into the T-1s to have them protect Skynet the moment it took control of the entire U.S. defense grid. It then killed Robert before going after John and Kate. They managed to trap her in a particle accelerator before going to Crystal Peak, where they were told Skynet's central core was located. The Terminatrix broke free of the accelerator and followed them, losing most of her polyalloy skin and half of her lower body in the process. She grabbed John, determined to complete her mission but a T-850 unit sent by Kate from the future destroyed them both with its remaining hydrogen fuel cell with a remark of "you are terminated."

Trivia

 * The Terminatrix become Thomas, and Twilight Sparkle's enemy in Thomas and Twilight Sparkle's Adventures of The Terminator III: Rise of the Machines.