Lesson Plan

Define function composition: (f ∘ g)(x) = f(g(x)), meaning "apply g first, then apply f to the result"

Evaluate composite functions numerically: given f(3) and g values, find f(g(x)) for specific inputs

Evaluate composite functions symbolically: given f(x) and g(x) as expressions, find f(g(x)) by substitution

Determine the domain of a composite function by ensuring the output of the inner function lies in the domain of the outer function

Interpret composite functions in context, connecting the chain of dependencies (e.g., temperature depends on height, height depends on time)

Distinguish composition from multiplication: f(g(x)) != f(x) * g(x) in general

HSF.BF.A.1.c

HSF.BF.A.1.c: (+) Compose functions. For example, if T(y) is the temperature in the atmosphere as a function of height, and h(t) is the height of a weather balloon as a function of time, then T(h(t)) is the temperature at the location of the weather balloon as a function of time.