Florida B.E.S.T. MA.912.F.3

MA.912.F.3 is a B.E.S.T. standard. These are the benchmarks under it.

• MA.912.F.3.1

  Given a mathematical or real-world context, combine two functions, limited to linear and quadratic, using arithmetic operations. When appropriate, include domai...

• 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...

• MA.912.F.3.3

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

• MA.912.F.3.4

  Represent the composition of two functions algebraically or in a table. Determine the domain and range of the composite function.

• MA.912.F.3.5

  Solve mathematical and real-world problems involving composite functions.

• MA.912.F.3.6

  Determine whether an inverse function exists by analyzing tables, graphs and equations.

• 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.3.8

  Produce an invertible function from a non-invertible function by restricting the domain.

• MA.912.F.3.9

  Solve mathematical and real-world problems involving inverse functions.

01

What Students Need to Do

Students combine functions by adding, subtracting, multiplying, dividing, or composing their rules. They also shift, reflect, or stretch graphs and track any new domain restrictions.

02

What Mastery Looks Like

Given formulas, tables, or graphs, students can build the requested function and find its outputs. They simplify the new rule, identify valid inputs, and explain how it relates to the original functions.

03

Common Misconceptions

Students often confuse f(g(x)) with f(x)g(x). They may reverse horizontal shifts, reading f(x + 3) as a shift right. They also forget restrictions created by denominators or square roots.

04

How to Assess It

Give f(x) = 2x + 1 and g(x) = x². Ask students to write and simplify (f + g)(x), f(g(x)), and f(x - 3), then describe the last change.

1. 01

   Use function-machine cards to connect two input-output rules, then build and test the composed function with three inputs.

2. 02

   Ask students to explain why f(x - 3) shifts a graph right, using an input-output example as evidence.

3. 03

   Run a card sort matching original functions, new equations, graphs, and transformation descriptions; teams explain each match before checking.

4. 04

   Combine a taxi-fare function with a percentage surcharge function, then calculate and interpret the final fare for three trips.

• MA.912.F.2

  Identify and describe the effects of transformations on functions. Create new functions given transformations.

• MA.8.F.1

  Define, evaluate and compare functions.