Florida B.E.S.T. MA.912.F.3.4
The Standard
Represent the composition of two functions algebraically or in a table. Determine the domain and range of the composite function.
Florida B.E.S.T. Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students substitute one function’s output into another function and show the result with a formula or input-output table. They find which inputs are allowed and which outputs the combined rule can produce.
What Mastery Looks Like
- A student correctly follows the stated order and builds the composite rule or table. They exclude invalid inputs and accurately describe all possible outputs.
Common Misconceptions
- Students reverse the order of the functions or add the rules instead of substituting. They use only the inner function’s domain and miss inputs that make the outer function undefined. They may assume the composite has the same range as one original function.
How to Assess It
- Exit ticket: Let f(x) = x² and g(x) = x − 3. Write f(g(x)), then state its domain and range.
Lesson moves
Ways to Teach It
Use two sets of function-machine cards so students pass inputs through both machines and record the composite input-output table.
Ask students to test when f(g(x)) and g(f(x)) differ, then explain why order matters.
Have pairs match cards showing a composite rule, value table, domain, and range, then defend each completed set.
Model a store discount followed by sales tax, then set realistic price limits and find the composite output range.
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Related Standards
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Represent the inverse of a function algebraically, graphically or in a table. Use composition of functions to verify that one function is the inverse of the oth...
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Solve mathematical and real-world problems involving composite functions.
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Given a set of ordered pairs, a table, a graph or mapping diagram, determine whether the relationship is a function. Identify the domain and range of the relati...
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Determine whether an inverse function exists by analyzing tables, graphs and equations.
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