In the Brass family we have:

French Horn
The French Horn in F which is a transposing instrument.  When it reads ‘C’, it sounds ‘F’, a perfect 5th lower. So this means  that for the instrument to sound in a certain key it must play in a key which is a perfect 5th higher.

For example if a musician  was composing an orchestral piece in the key of D major and wished to include the French Horn in F, he would have the French Horn play in the key of A, a perfdect 5th higher.  Then, as explained above, the Horn will sound a perfect 5th lower and therefore in the key of D.

It must be mentioned here that the French Horn never has a key signature.  Instead, the accidentals are written in front of the notes.

Trumpet
The Trumpet can also be a transposing instrument.  There are various different ones but I am considering the E Trumpet as an example.  This is because it is included in the score, Tchaikovsky’s Romeo and Juliet for Leaving Cert Course A .

When the Trumpet in E reads ‘C’, it sounds  E, a major 3rd higher.  So this means  that for the instrument to sound in a certain key it must play in a key which is a major 3rd lower.

For example if a musician  was composing an orchestral piece in the key of F major and wished to include theTrumpet in E, he would have the Trumpet play in the key of D flat, a major 3rd lower.  Then, as explained above, the Trumpet will sound a major 3rd higher, therefore in the key of F.

It must be mentioned here that the Trumpet, as the French Horn never has a key signature.  Instead, the accidentals are written in front of the notes.

One can get a trumpet in C which is not transposing.

Trombone
The Trombone is not a transposing  instrument, because it sounds as it reads.  When it reads ‘C’ it sounds ‘C’.  Also the thombone has a key signature, unlike the French Horn and Trumpet.

Tuba
The Tuba, the lowest of the Brass family is also non transposing.  It sounds as it reads, but an octave lower.  This does not make it transposing.  The Tuba, as the Trombone has a key signature too.

Note: Any instrument in ‘C’ is not transposing.