Florida B.E.S.T. MA.912.F.3.6
The Standard
Determine whether an inverse function exists by analyzing tables, graphs and equations.
Florida B.E.S.T. Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students decide whether reversing input and output values still produces a function. They use repeated outputs, the horizontal line test, or algebraic reasoning to support the decision.
What Mastery Looks Like
- Students correctly identify repeated outputs in a table, multiple intersections on a graph, or equal outputs from different inputs in an equation. They justify each decision and can suggest a domain restriction when needed.
Common Misconceptions
- Students often confuse an inverse function with a reciprocal, writing 1/f(x). They may use the vertical line test instead of the horizontal line test. They may also ignore the stated domain when deciding whether outputs repeat.
How to Assess It
- Exit ticket: For f(x) = x² - 4 on all real numbers, decide whether its inverse is a function. Justify your answer and give a domain restriction that would change the result.
Lesson moves
Ways to Teach It
Give pairs sticky notes showing inputs and outputs, then have students reverse each pair and check whether any reversed inputs repeat.
Ask students to explain why f(x) = x² fails on all real numbers but works when x is restricted to x ≥ 0.
Run a card sort matching tables, graphs, and equations with labels reading inverse is a function or inverse is not a function.
Compare Celsius conversion with a tossed ball's height over time, then decide which relationship can be reversed into a function.
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- MA.912.AR.8.2
Given a table, equation or written description of a rational function, graph that function and determine its key features.
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Solve mathematical and real-world problems involving inverse functions.
- MA.912.AR.2.4
Given a table, equation or written description of a linear function, graph that function, and determine and interpret its key features.
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