Common Core Math
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Learning Goal

Part of: Build a function that models a relationship between two quantities — 4 of 5 cluster items

Compose functions

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.

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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

  1. Define function composition: (f ∘ g)(x) = f(g(x)), meaning "apply g first, then apply f to the result"
  2. Evaluate composite functions numerically: given f(3) and g values, find f(g(x)) for specific inputs
  3. Evaluate composite functions symbolically: given f(x) and g(x) as expressions, find f(g(x)) by substitution
  4. Determine the domain of a composite function by ensuring the output of the inner function lies in the domain of the outer function
  5. Interpret composite functions in context, connecting the chain of dependencies (e.g., temperature depends on height, height depends on time)
  6. Distinguish composition from multiplication: f(g(x)) ≠ f(x) · g(x) in general

Slides

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Slides

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