model a situation using function notation when the output of one function is the input of a second function such as determining a function ℎ(?) = ?(?(?)) = 1.06(0.8?) for the final purchase price, ℎ(?) of an item with price ? dollars representing a 20% discount, ?(?) = 0.8? followed by a 6% sales tax, ?(?) = 1.06?; and
Patterns and structure. The student applies mathematical processes to understand the connections among representations of functions and combinations of functions, including the constant function, 𝑓(𝑥) = 𝑥, 𝑓(𝑥) = 𝑥², 𝑓(𝑥) = √𝑥, 𝑓(𝑥) = 1/𝑥, 𝑓(𝑥) = 𝑥³, 𝑓(𝑥) = ³√𝑥, 𝑓(𝑥) = 𝑏 to the 𝑥 power, 𝑓(𝑥) = |𝑥|, and 𝑓(𝑥)=𝑙𝑜𝑔 𝑏𝑎𝑠𝑒-𝑏 (𝑥) where 𝑏 is 2, 10 or 𝑒; functions and their inverses; and key attributes of these functions.