Learn Farsi: من تازه متوجه گرانی این ماشین شده‌ام. - I have just realized the high price of this car.

Adding the suffix -i to an adjective turns it into an abstract noun. So, the adjective gerān (expensive) becomes the noun gerāni (expensiveness or high price). You are literally saying I have just realized the expensiveness of this car.

Doesn't tāze usually mean fresh? How does it translate to just here?

Yes, as an adjective tāze means fresh (like fresh bread). But when used as an adverb before a verb, as it is here, it means recently, newly, or just. It is very commonly used in spoken and written Farsi to talk about things that have just happened.

The verb is motevajeh shodan (to realize). How does motevajeh connect to the object gerāni?

It connects using the ezafe (the invisible short 'e' sound). The compound verb motevajeh shodan links to its object directly with this sound, rather than using a preposition like az (from/of). When speaking, you will say motevajeh-e gerāni.

Does that mean there is a chain of ezafe sounds in this sentence?

Exactly! The phrase is pronounced motevajeh-e gerāni-ye in māshin. The first ezafe links the realization to the high price, and the second one (pronounced -ye because gerāni ends in a vowel) links the high price to this car.