Lip Slurs are an essential part of practicing. They keep our lips strong and flexible. Lip slurs help our embouchure stay consistent as well (ie, we have the same embouchure for all notes), so as a student's range expands, the lip slur exercises' range can also expand.
Below are three lip slurs for beginning, intermediate, or advanced students.
1). Breathe in, breathe out. Imagine that your breath is always moving in one direction or the other. Never "hold" your air stationary. Correct breathing keeps your body relaxed.
2). Your ideal air stream (the air you move from your lungs into the mouthpiece when you play) is a very narrow stream of very fast air. Imagine the diameter of your air stream as the diameter of the end of your mouthpiece (it is not the diameter of the mouthpiece cup, but the back side).
3). Arch your tongue as you move up to higher notes to create the smooth lip slurs. Say "ee" in your mouth (not with your lips) as you move higher up, and "aah" as you move down to lower notes, gradually dropping your jaw and your tongue.
Beginners can practice one lip slur a day, switching to a new lip slur every few weeks. More advanced players can practice at least two different lip slurs each day, with increasing complexity and range and switching more frequently between different exercises.
I also encourage advanced students to make up their own lip slurs-- it can add a fun, new dimension to your lip slurs if you create your own pitch order and rhythm!
Horn teacher and performer