Florida B.E.S.T. MA.912.F.3.3

MathGrades 9–12Create new functions from existing functions.

The Standard

Solve mathematical and real-world problems involving functions that have been combined using arithmetic operations.

Florida B.E.S.T. Standards for Mathematics

Teacher's field guide

What Students Need to Do: Students combine two functions by adding, subtracting, multiplying, or dividing their outputs. They evaluate the new function and use it to solve a mathematical or real-world problem.
What Mastery Looks Like: Students correctly write and evaluate sums, differences, products, and quotients of functions from equations, tables, or graphs. They select the right operation for a situation and identify restrictions on quotients.
Common Misconceptions: Students may confuse adding functions with composing them, treating (f + g)(x) as f(g(x)). They may multiply formulas incorrectly or forget that a quotient is undefined when the denominator equals zero.
How to Assess It: Exit ticket: Let f(x) = 2x + 5 and g(x) = x - 3. Find (f + g)(4), write (f/g)(x), and state the excluded x-value.

Lesson moves

Give pairs of function cards and input cards, then have students calculate the sum, difference, product, and quotient outputs.
Ask students to explain how (f + g)(x) differs from f(g(x)), using one numerical example.
Play a matching game where students pair combined-function expressions with simplified formulas, values, and domain restrictions.
Model profit as revenue minus cost, then have students calculate profit for several sales amounts and explain what negative results mean.

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