Answer:
From ages 5 to 8:
Pattern rule: Add 6 inches each year, since Fardad grows 6 inches each year.
Linear function:

From ages 8 to 10, not including 8:
Pattern rule: Add 11 inches each year, since Fardad grows 11 inches each year.
Linear function:
Explanation:
Pattern rule seems subjective and I don't believe there is a technical mathematical term for it, but in terms of linear functions and patterns:
From ages 5 to 8:
, where
is Fardad's height after age

Pattern from ages 5 to 8: Fardad grows 6 inches each year (add 6 each year)
From ages 8 to 10, not including 8:
, where
is Fardad's height after age

Pattern from ages 8 to 10, not including 8: Fardad grows 11 inches each year (add 11 each year)