Florida B.E.S.T. MA.912.F.1.9
The Standard
Determine whether a function is even, odd or neither when represented algebraically, graphically or in a table.
Florida B.E.S.T. Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students compare outputs at opposite inputs, x and -x. They use those values or graph symmetry to classify a function as even, odd, or neither.
What Mastery Looks Like
- A student correctly applies f(-x)=f(x) or f(-x)=-f(x) without sign errors. From graphs and tables, the student checks y-axis or origin symmetry and cites evidence.
Common Misconceptions
- Students often confuse origin symmetry with x-axis symmetry. They may substitute -x incorrectly, check only one input pair, or ignore whether the domain includes opposite inputs.
How to Assess It
- Exit ticket: classify f(x)=x²+x, a sketch of y=|x|, and the table x: -2, -1, 1, 2; f(x): -5, -2, 2, 5. Cite the symmetry or value test for each.
Lesson moves
Ways to Teach It
Give pairs patty paper to fold graphs across the y-axis, then rotate them 180 degrees around the origin and record matches.
Ask students to write why f(x)=x⁴+2 and g(x)=x³-2x have different symmetries, using equations and graph language.
Run a card sort with algebraic rules, graphs, and tables; students place each under even, odd, or neither and defend one choice.
Model a hill with h(x)=20-x², then compare heights at positions equally far left and right of the summit.
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Related Standards
- MA.3.AR.3.1
Determine and explain whether a whole number from 1 to 1,000 is even or odd.
- MA.2.AR.3.1
Represent an even number using two equal groups or two equal addends. Represent an odd number using two equal groups with one left over or two equal addends plu...
- MA.912.F.1.7
Compare key features of two functions each represented algebraically, graphically, in tables or written descriptions.
- MA.912.F.3.6
Determine whether an inverse function exists by analyzing tables, graphs and equations.
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