Florida B.E.S.T. MA.912.F.3.1
The Standard
Given a mathematical or real-world context, combine two functions, limited to linear and quadratic, using arithmetic operations. When appropriate, include domain restrictions for the new function.
Florida B.E.S.T. Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students combine linear and quadratic functions by adding, subtracting, multiplying, or dividing their expressions. They simplify the new rule and identify inputs that must be excluded.
What Mastery Looks Like
- Students correctly add, subtract, multiply, or divide the function expressions and simplify the result. They exclude denominator zeros and apply any limits created by the context.
Common Misconceptions
- Students may confuse f(x)g(x) with function composition or multiply only one term. They may divide by zero, overlook excluded inputs, or apply context limits to the wrong function.
How to Assess It
- Give f(x)=2x+3 and g(x)=x²-4. Ask students to find (f+g)(x) and (f/g)(x), then state each domain.
Lesson moves
Ways to Teach It
Give pairs index cards with linear and quadratic functions, then have students build and simplify each arithmetic combination on chart paper.
Ask students to explain why the domain of f(x)/g(x) may differ from the domains of f and g.
Play a matching game with cards showing function pairs, operations, simplified results, and domain restrictions.
Model revenue minus quadratic cost to create a profit function, then identify the meaningful domain from production limits.
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Related Standards
- MA.912.F.3.3
Solve mathematical and real-world problems involving functions that have been combined using arithmetic operations.
- MA.912.AR.3.9
Given a mathematical or real-world context, write two-variable quadratic inequalities to represent relationships between quantities from a graph or a written de...
- MA.912.F.3.5
Solve mathematical and real-world problems involving composite functions.
- MA.912.F.3.2
Given a mathematical or real-world context, combine two or more functions, limited to linear, quadratic, exponential and polynomial, using arithmetic operations...
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