This looks like two adjectives, steep and horizontal, masquerading as adverbs. I believe it should be phrased as 'starting steeply' and 'leveling off horizontally'. They both refer to 'how'. These two words, steep and level follow a verb, therefore they become adverbs. I just checked this at Dictionary.com. Also, I learned English when the subject was rigorously taught.
Adverb: A word or phrase that modifies or qualifies an adjective, verb, or other adverb or a word group, expressing a relation of place, time, circumstance, manner, cause, degree, etc. Origin - late Middle English: from Latin adverbium, from ad- ‘to’ (expressing addition) + verbum ‘word, verb.’.