absagen
to cancel
To cancel or declare invalid a scheduled appointment, event, or arrangement.
Wegen Krankheit musste sie das Konzert leider absagen.
Because of illness, she unfortunately had to cancel the concert.

to cancel
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to cancel
To cancel or declare invalid a scheduled appointment, event, or arrangement.
Wegen Krankheit musste sie das Konzert leider absagen.
Because of illness, she unfortunately had to cancel the concert.

'Absagen' (to cancel/decline) is a separable verb. The prefix 'ab-' goes at the end of the main clause. In subordinate clauses and in the infinitive with 'zu', the verb stays together.
Ich sage den Termin für morgen ab.
I am canceling the appointment for tomorrow.
When you cancel something planned, 'absagen' (to cancel) needs an accusative object. Typical objects are: 'einen Termin' (an appointment), 'eine Reise' (a trip), 'eine Party' (a party), or 'ein Treffen' (a meeting).
Wir mussten unseren Flug wegen des Streiks absagen.
We had to cancel our flight because of the strike.
When declining an invitation, 'absagen' (to decline) can also be used without an object. The context then makes clear what it refers to.
Danke für die Einladung, aber ich muss für Samstag leider absagen.
Thanks for the invitation, but unfortunately I have to decline for Saturday.
When you give a person a negative answer (e.g., to an application), the person is put in the dative. The structure is: 'jemandem absagen' (to turn someone down).
Die Firma hat ihm leider für die Stelle abgesagt.
The company unfortunately turned him down for the position.
to accept / assume
'annehmen' and 'absagen' are opposites when it comes to an invitation or an offer. With 'annehmen', you say yes and accept the offer. With 'absagen', you say no, for example to an invitation or an appointment. 'absagen' can also mean that a planned appointment or event does not take place. But for the direct opposite of 'annehmen', the important point is: you receive an offer and decide against it.

Wegen einer Krankheit sagt Sofia die Einladung zur Feier ab.
Because of an illness, Sofia declines the invitation to the party.
Tom nimmt das Angebot für den Wochenendkurs an.
Tom accepts the offer for the weekend course.