つづける・ていく: the difference
つづけるN4
Meaning
To continue
Past papers
Tested once in past papers
Example
テレビを見続けるつもりですか。
Do you plan to continue to watch TV?
ていくN4
Meaning
To ~ and go, To go on, To start
Past papers
Example
大きい音で、鳥が飛んでいく。
At the loud noise, the birds fly away.
How to tell them apart
Versus 「〜ていく」: 「〜つづける」 looks at going on without a break from the past or now; 「〜ていく」 looks at developing from now toward the future.
As a compound, 「〜続ける」 works with most verbs, even for things that happen by themselves (「雨が降り続ける」). 「〜続く」 combines with only a few verbs (「降り続く」「鳴り続く」) and is more written.