～おかげで— Thanks To

• 先生のおかげで合格できました。

  Sensei no okage de goukaku dekimashita.

  Thanks to my teacher, I was able to pass.

  Noun 先生 + の + おかげで credits the teacher for the positive result of passing.

• 薬を飲んだおかげで、熱が下がった。

  Kusuri o nonda okage de, netsu ga sagatta.

  Thanks to taking the medicine, my fever went down.

  Verb past 飲んだ + おかげで links the cause to a welcome outcome.

• 天気がよかったおかげで、旅行を楽しめた。

  Tenki ga yokatta okage de, ryokou o tanoshimeta.

  Thanks to the good weather, we could enjoy the trip.

  い-adj past よかった + おかげで attributes the enjoyable trip to good weather.

• ・Default nuance is positive gratitude.
• ・おかげさまで is a set humble phrase for 'thanks to you / thankfully'.
• ・Can be ironic ('thanks a lot...') but context makes this clear.

Commonly confused with

The JLPT rarely asks whether you recognise a pattern — it asks which of several similar patterns fits. These are the ones ～おかげで is tested against.

• ～あまり(に) — So Much That It Overwhelms
• ～せいで — Because Of (And I Blame It)
• ～せいか — Perhaps Because Of
• ～からといって — Just Because
• ～ことから — Judging From The Fact
• 次第だ／次第で — It All Depends
• だけあって — Living Up to It
• ～につれて — As One Thing Changes, So Does Another