に応(おう)じて is a combination of に, and the て-form of the る-Verb 応(おう)じる ‘to apply to’. This grammar structure is often translated as ‘depending on (A), (B)’, or ‘in response to (A), (B)’. However; in almost all cases, it is just indicating that (B) is something that is done in a way that is ‘applicable’ to what is necessary of (A).
に応(おう)じて will appear after nouns, or as
に応(おう)じた when directly modifying a second noun.
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日本語(にほんご)を教(おし)える際(さい)には、生徒(せいと)達(たち)のレベルに応(おう)じてクラスを分(わ)ける必要(ひつよう)があります。
When teaching Japanese, it is necessary to divide classes according to the level of the students.
この地域(ちいき)の土地(とち)は、面積(めんせき)に応(おう)じて値段(ねだん)が高(たか)くなります。
Land in this area is priced according to its surface area.
私(わたし)たちはクライアントの要望(ようぼう)に応(おう)じたデザインを提供(ていきょう)しています。
We provide designs that meet our clients' requests.
Fun-fact - 応(おう)じる usually indicates the way something ‘responds to’ or ‘answers’ an issue on a case-by-case basis. Due to this, what happens in (B) will frequently indicate something that changes depending on the intensity or severity of (A).