Compose functions

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Lesson Plan →Objectives, pacing and practice, built from this lesson's brief.
Guided Notes →One page your students fill in and keep.
Exit Ticket →Three items at the end of class. No student accounts.
Re-teach →After an exit ticket: who missed what, and what to do tomorrow.
Homework →Assign practice; it grades itself.

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.

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.

What you'll learn

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

Review first:

Combine function types

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Compose functions

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Exercise

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