stetig
steady
Continuous and even, proceeding without interruptions or major fluctuations.
Die Bevölkerungszahl der Stadt verzeichnet ein stetiges Wachstum.
The city's population is showing steady growth.

steady / continuous
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steady
Continuous and even, proceeding without interruptions or major fluctuations.
Die Bevölkerungszahl der Stadt verzeichnet ein stetiges Wachstum.
The city's population is showing steady growth.

'Stetig' is related to the adverb 'stets' (always). Both words express a form of constancy or duration. A 'stetige Entwicklung' (steady development) is one that always moves in the same direction.
Die Kosten sind stetig gestiegen.
Costs have risen steadily.
'Stetig' can stand before a noun as an adjective or describe a verb as an adverb. As an adverb, its form remains unchanged.
Wir beobachten eine stetige Verbesserung der Situation.
We are observing a steady improvement in the situation.
In its general meaning, 'stetig' is often used to describe trends. Common combinations include 'stetiges Wachstum' (steady growth), 'stetige Zunahme' (steady increase), 'stetig steigen' (to rise steadily), or 'stetig sinken' (to fall steadily).
Die Nachfrage nach Elektroautos wächst stetig.
Demand for electric cars is growing steadily.
The meaning of 'stetig' in connection with functions is a technical term from mathematics. Outside this context, the word is almost never used this way.
Der Dozent erklärte, warum diese Funktion nicht stetig ist.
The lecturer explained why this function is not continuous.
constant
'ständig' and 'stetig' can both express that something happens without major interruption. The difference lies in the feeling and the way it develops. 'ständig' often means very frequently or constantly, and sometimes sounds a bit annoyed, for example with noise or questions. 'stetig' means steady and calm, often with a development that continues slowly. Learners may confuse the words because both have to do with duration. Remember: 'ständig' fits often repeated events, while 'stetig' fits a steady change.

Die Zahl der Besucher steigt seit Wochen stetig.
The number of visitors has been steadily increasing for weeks.
Mein Nachbar ruft ständig an, obwohl ich gerade arbeite.
My neighbor keeps calling, even though I am working right now.