<transcript><audio_15>this is the function y equals the log base 6 of X you think I want to eventually reach an infinity here as it climbs yes it will I mean it'll take a long time because I'll rate will slow over time but it'll get there and down</transcript><transcript><audio_16>here this is plummeting really quick towards negative infinity and so the range is taking all real numbers from negative into positive infinity and essentially everything that's in between</transcript><transcript><audio_17>so the range would not include all real numbers if there was some have limitation like an asymptote or something that I couldn't reach but logarithms typically will the range will be the set of all real numbers all right</transcript> this is the function y equals the log base 6 of X you think I want to eventually reach an infinity here as it climbs yes it will I mean it'll take a long time because I'll rate will slow over time but it'll get there and down here this is plummeting really quick towards negative infinity and so the range is taking all real numbers from negative into positive infinity and essentially everything that's in between so the range would not include all real numbers if there was some have limitation like an asymptote or something that I couldn't reach but logarithms typically will the range will be the set of all real numbers all right
{"source": "grass-yt-cc-by.-TLGJXJtdus|shard_10036_44|create_multimodal_data.extract_yt_and_generate_transcripts.41|shard_10036|create_multimodal_data.generate_captions.32|shard_10036|create_multimodal_data.generate_captions.32", "params": {"id": "-TLGJXJtdus", "channel_id": "UC5EVHEptldG1XGBrLXq-wLw", "duration": 225, "view_count": 202, "age_limit": 0, "like_count": 2, "channel_follower_count": 13400, "license": "Creative Commons Attribution license (reuse allowed)", "uploader_id": "@shaunteaches", "yt_tar_file": "/leonardo_work/EUHPC_E03_068/audio/fixed_download/grass-yt-cc-by//shard_10036/-TLGJXJtdus.tar.gz"}}