Composition of Functions Worksheet

Composition of Functions Worksheet Generator

Choose a topic and options, then print the worksheet. Each worksheet comes with its own answer key.

Answer key
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Types of composition of functions worksheets you can make

  • Evaluating compositions: find values like f(g(2)) or (f ∘ g)(2) from two function rules
  • Finding the composite function: write f(g(x)) or g(f(x)) as one function in standard form
  • Tables of values: read f(g(3)) from a table of x, f(x) and g(x) values
  • Graphs: read compositions like g(f(−1)) from the graphs of f and g
  • Function machines: follow a number through two or three machines and fill in the missing numbers
  • Working backward: use a function machine to find the input that gives a certain output
  • Composing a function with itself: f(f(x)) and g(g(4))
  • Three functions: f(g(h(x))) and (f ∘ g ∘ h)(2)
  • Decomposing functions: given h(x) = (3x − 1)², find f and g so that h(x) = f(g(x))

Make each worksheet your own:

  • four difficulty levels, from two linear functions up to quadratics and fourth-degree answers
  • write problems as f(g(x)), as (f ∘ g)(x), or mix both
  • choose how many problems to include
  • every worksheet comes with an answer key that shows the steps

Composite function