Florida B.E.S.T. MA.912.F.3.8
The Standard
Produce an invertible function from a non-invertible function by restricting the domain.
Florida B.E.S.T. Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students identify a part of a graph where each output comes from only one input. They choose and state a restricted domain, then verify it with the horizontal line test.
What Mastery Looks Like
- For f(x) = x², a student can choose x ≥ 0 or x ≤ 0 and explain why either choice works. The student states the restriction clearly and confirms that outputs no longer repeat.
Common Misconceptions
- Students may restrict the range instead of the domain. They may choose an interval that still repeats outputs, or think there is only one valid restriction.
How to Assess It
- Exit ticket: For f(x) = (x − 2)² − 3, give one domain restriction that makes the function one-to-one. Explain using the horizontal line test.
Lesson moves
Ways to Teach It
Give pairs a printed parabola and sticky notes to cover sections until every horizontal line meets the visible graph at most once.
Ask students to explain why x ≥ 0 works for f(x) = x² and why x ≥ −2 does not.
Run a card sort matching non-invertible graphs with domain restrictions that make each graph one-to-one.
Graph a ball’s height over time, then restrict time to either its rise or fall so each height matches one time.
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Related Standards
- MA.912.F.3.7
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...
- MA.912.F.1.2
Given a function represented in function notation, evaluate the function for an input in its domain. For a real-world context, interpret the output.
- MA.912.C.2.6
Find derivatives of inverse functions.
- MA.912.F.3.9
Solve mathematical and real-world problems involving inverse functions.
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